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.]
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).