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Are different varieties of German (e.g. Bavarian and Low German) closer to each other than different Slav languages (e.g. Russian and Polish)?
The lexical distance map from https://elms.wordpress.com/2008/03/04/lexical-distance-among-languages-of-europe/
seems relevant here, but doesn't cover different varieties of German. I'm also not sure this map is accurate.
Are different varieties of German (e.g. Bavarian and Low German) closer to each other than different Slav languages (e.g. Russian and Polish)?
Yes,
Are the most distant German dialects/languages closer to each other than Russian to Polish? Yes, all German dialect/languages are closer to each other than the difference between those two.
No,
Are the most distant German dialect/language e.g. Plattdüütsch to Boarisch closer to each other than Croatian to Serbian? No, Serbian and Croatian are closer to each other than Plattdüütsch to Boarish.
and Maybe
Is Plattdüütsch to Boarisch closer to each other than Czech to Slovak? Maybe, you would have to research it to tell.
Speaking just about my own personal experience:
I can only understand a little Russian because of the similarities I can find from two other Slavic languages I speak: Ukrainian and Polish. As someone who has never been exposed to Russian before, I feel that I would not be able to understand Russian with just one of the other Slavic languages. Therefore, I don't feel that I can agree with the notion of Russian/Polish understanding. In fact, I feel that this might even be a cultural misconception, as I've had quite a few experiences where Russian speakers insist on speaking Russian at me, convinced that I will 'magically' understand them. I've also noticed that non-Slavic speakers believe this as well.
however, in the Czech Republic, speaking Polish will get me nowhere, but speaking Ukrainian will get me by quite well indeed. Again, I'd like to stress that is just personal experience.
You later edited in your question that you're not interested in whether speakers of the varieties can understand each other, but unfortunately that's exactly the definition that is predominantly used to draw the line between a language and a dialect, so I'll stick to my anwer as I had it before and leave it to other answerers to provide different approaches, like statistical analysis of lexical similarity.
That the German varieties are mostly considered dialects while the Slavic languages are languages already implies that the former are significantly closer to each other.
Even if two Germans from different regions speak speak a very strong dialect (which is nowadays a marginal, mostly rural phenomenon), two Germans from different dialects would still understand each other to large extent, even more so when they try to be cooperative and both simply speak their "Dachsprache" which makes communication entirely unproblematic.
The differences lie mostly in phonetics and phonology; lexicon is sporadically different (esp. food names), but almost entirely shared; grammar is essentially the same across dialects except for some individual deviations on special constructions, which are, however, still very compatible with what is perceived as Standard German.
You can of course always make things unnecessary complicated by putting emphasis on the features that are not shared with the other dialects, but that's not what mutual intelligibility (the ability to communicate with each other) is about. I would argue that even a Bavarian and a speaker of Low German can understand each other if they want, although of course this might not be as simple as, say, between a Swabian and a Badensian.
This is not so easy for, e.g., Russian and Polish, which have lexical and grammatical similarities but are not so easily mutually intelligible even if two speakers try to make themselves easily understandable to the other. Reading is probably easier because the differences in phonetics and phonology don't manifest themselves as heavily as in speech, but you would still consider them different languages because there are too major divergences in terms of grammar and lexicon, although there is some overlap.
I find michau's comment "If it's easier to speak an unrelated third language (e.g. English), it means that the languages aren't mutually intelligible" quite a good approximation here - I've frequently heard Russians and Bulgarians, Polishs, ... talk English to each other because this was the easiest way to communicate for them, but it would be extremely unlikely that two speakers of German find their respective dialects so unintellegible they'd rather talk in English (even if they spoke English well) than in their native language to each other.
So while there is a lot of political discussion to that issue that I really don't want to go into here, considering the above I would claim that German (not Germanic!) varieties are to be considered closer to each other than are Slavic varieties.
I think this is a very interesting question. Even though the question is very hard to answer, I don't quite agree with the statements about the Germanic side.
If you're taking into account Low German, then you could also research the mutual intelligibility of German and Dutch because it should be very similar. (In some ways Dutch and German are more alike (raising of *ō and *ē to /uː/ and /iː/, *eu > ie > /iː/ diphthongisation of î/ij and û,ü/ui) and in some ways German and Low German (many umlauts)). The reason why Low German is sometimes seen as a German dialect is partially political. Apart from "Überdachung" (Dachsprache) by the High German standard language Low German has the same relationship to German that Dutch has. (Here you can easily see that the lexical distance map groups together varieties that shouldn't be grouped together while keeping others seperate.)
https://en.wikipedia.org/wiki/Mutual_intelligibility doesn't even list partial intelligibility between German and Dutch. But for example "Russian: Belarusian and Ukrainian (both partially)"
"Speakers of languages within the same branch[of the Slavic language family] will in most cases be able to understand each other at least partially, but they are generally unable to across branches" (https://en.wikipedia.org/wiki/Slavic_languages)
Assuming the information is consistent and comparable that would allow us to estimate that Low German and German are more different than Russian, Belarusian and Ukrainian but less so than Russian and Polish.
[Edit: They might even be more different than Belarusian/Ukrainian and Polish, because Wikipedia also mentions considerable difficulties in the mutual intelligibility of spoken Dutch and German, whilst for spoken Polish, Belarusian and Ukrainian partial intelligibility is listed again.]
[Edit:
And I should add that while there are no High German dialects quite as different from Standard German as Low German, you could probably make the same argument for many High German dialects.
Comparing the information on en.wikipedia.org/wiki/Mutual_intelligibility again, you could estimate that Luxembourgish is as different from Standard German as Russian, Belarusian and Ukrainian are. That would exemplify that even High German dialects (here Luxembourgish is only in so far different as it is standardized) are as different as Slavic languages. (In case you are confused by my usage of the term "High German", consider looking it up.)
]
[I've decided that I should post the comments I made to lemontree's answer as an individual answer, since it offers a different perspective than the other answers and since lemontree's answer already has so many comments that very few people would read them:]
Lemontree: "I would argue that even a Bavarian and a speaker of Low German can understand each other if they want, although of course this might not be as simple as, say, between a Swabian and a Badensian."
I would argue that is only true if they know Standard German or don't actually speak true Low German or Bavarian. Since the former is practically always true, you can't compare the similarity of the dialects via mutual intelligibility because the speakers know a third language that helps with the intelligibility. If we still had the situation that people only spoke their home towns' dialect in Germany, it would need a lot of exposure for them to understand each other.
Also I've often heard the statement that German and Dutch aren't mutually intelligible. If that's true then that would be proof that Bavarian and Low German aren't mutually intelligible. I have no doubt that spoken German and Dutch are more similar than Low German and Bavarian.
On the other hand, there are good reasons not to consider Low German a variety of "German" (I would even argue that the Bavarian dialect isn't a variety of "German". It is a High German dialect, sure, but it's relationship to German might be the same that Scots has to English).
Since I don't have any other source at hand: "By early modern times, the span had extended into considerable differences, ranging from Highest Alemannic in the South […] to Northern Low Saxon in the North. Although both extremes are considered German, they are not mutually intelligible. The southernmost varieties have completed the second sound shift, whereas the northern dialects remained unaffected by the consonant shift." (wikipedia.org/wiki/West_Germanic_languages#Middle_Ages) And I would say Alemannic is closer to Low German than Bavarian (/yː, øː/, no i-,u-diphthongisation).
