Ideally, one should first determine the construction method and then find the suitable craftsmen. Only if there are other constraints should one follow the construction method of the designated [GU/Bauträger].
Especially since there are many GU/GÜ who do not build themselves at all. They simply look for the cheapest construction company that will provide them with the shell construction.
It is a myth that GUs always and constantly work with the same craftsmen. They also look for the cheapest craftsman who is available at the time.