The difference isn't really to do with some subtle distinction between the meanings or associations of manifest and embody (or derivatives thereof). It's more the fact that #1 includes an indefinite article.
Thus #1 implies there are other manifestations (this particular instance being just one of many), whereas #2 implies that the wisdom of specialist architectural design institutions is a single clearly-defined thing (perhaps with the further implication that people who know about such things have very precise ideas about what exactly that wisdom is, and how to recognise it or put it into practice).
To illustrate this, I suggest exactly the opposite distinction applies if we reverse the "noun / verb" usages...
3: ...the music hall manifests the wisdom of specialist architectural design institutions.
4: ...the music hall is an embodiment of the wisdom of specialist architectural design institutions.
Having said that, it would also be possible to use the definite article...
5: ...the music hall is the manifestation of the wisdom of specialist architectural design institutions.
6: ...the music hall is the embodiment of the wisdom of specialist architectural design institutions.
On purely idiomatic grounds, #5 is less likely (it comes across as slightly "clumsy" to me), but in terms of "subtle implications", using the definite article is closer to using the verb form in both cases.
For most purposes, all these examples would be seen as just different ways of saying the same thing - but there are subtle distinctions that can be "reasoned out". A "careful" writer might take these into consideration in certain contexts. Don't over-think it though. It doesn't really make much difference.