Matthias.
There is nothing “wrong” with the name Felix, but I always think of how a name will play when the child (especially if the child is a boy) is in school — what I call a “playground-proof” name. Felix is somewhat of an unusual name (in our society) and you also have the prissy Felix Unger character from The Odd Couple. (Granted, most children would never even have heard of this show.) Matthias shortens very efficiently to Matt, and the worst thing you can do with that name is morph it into “door mat”.
Boys have a hard enough time in our culture as it is. And yes, I have experience with this sort of thing — I had the task of naming a son, and I gave him a name that is strong, biblical, and undeniably masculine. It fits him well.