The adjective systems in Balto-Slavic and German languages are similar only from a very broad typological and historical point of view.
Most Slavic languages — I can speak about Russian, but it must not be too different elsewhere — have a special morphological paradigm (i.e. a set of endings) for the adjectives when they stand in the modifier position with respect to a noun. These endings are originally of pronominal origin. Effectively, they come from a relative pronoun agglutinated to the nominal stems (see on this Meillet, Le Slave commun, 1934: §509).
When the adjective is a predicate, it takes a nominal ending, which is shorter (hence they are called "short adjectives") and is only realized in the Nominative (since the predicate is always in the Nominative). In Russian the short adjectives are gradually fading out, while the adjectival endings are being used more and more also in the predicative position. Compare the following constructions.
Predicative position (the nominative is marked by a zero-ending: Ø)
Судья строг, но справедлив.
Sudj-a strog-Ø, no spravedliv-Ø
Judge-NOM strict-NOM but fair-NOM
"The judge is strict but fair"
Modifier position (note the longer endings of the adjectives glossed here as ADJNOM)
Строгий, но справедливый судья
strog-ij, no spravedliv-yj sudj-a
strict-ADJNOM but fair-ADJNOM judge-NOM
"a fair but strict judge"
At the beginning, when these forms had been created, the intended function of those agglutinated pronouns was probably to encode the definitiveness (as claimed by Meillet). However, we have no certainty on that. Today these endings have simply become the adjectival endings.
On the other hand, the so-called "strong declension" was attested in all the ancient Germanic languages (from Gothic to Old English, Old Norse and Old High German) and survives today just in some of them (notoriously in German). In Modern German it has to do with definiteness, but, again, we are not allowed to automatically imply the same function for the ancient languages. Whatever it might be, the Gothic declension of the adjective is vaguely similar to the modern German usage: the weak endings are used when the article is present, while the strong endings are used elsewhere. See, for example, the following line from the Lord's Prayer (note the glosses wACC "weak Accusative" vs. sACC "strong Accusative"):
hlaif unsar-ana þ-ana sintein-an (gif uns himma daga)
bread-ACC ours-sACC the-sACC dayly-wACC (give us this day)
Notice that the bare adjective unsarana has the strong, i.e. pronominal ending, same as the article þana; on the other hand, the adjective sinteinan has the weak ending, since it is preceded by the article.
Now, Germanic strong endings have clearly a pronominal origin (see this paper by McFadden). This makes them appear, for a specialist in Indo-European linguistics, as a parallel phenomenon to the adjectival declension in Balto-Slavic. The first to notice this parallelism was already Leskien (Die Declination im slavisch-litauischen und germanischen, 1876: p. 130ff). But we don't know much more than this. And in the modern usage this parallelism has been totally dimmed. For example, while the strong endings in Gothic were used in the predicative position, the "longer" adjectival endings in Slavic are excluded from exactly that same position. Moreover, modern Germanic languages have the article, while most of the Modern Slavic don't; therefore, the German construction differs from a possible Slavic parallel construction at least because of this lack.
P.S. By coincidence I have right now presented a paper on exactly this topic, see here.