Based on my own personal opinion and experiences? Fischer random creates a lot of uncertainty in my mind when I play. Regardless of what obscure opening is played in a traditional game I still have a sense of what spaces are likely to be controlled by rooks, where I can anticipate a knight showing up and so forth.
As far as your statement regarding branching factor increase can you point me to some references? Its not that I do not believe you I'm curious at what point the complexity begins to take off.
As a serious player with a reasonable amount of experience with both variants I have to say I disagree with you profoundly on this. FischerRandom/Chess960 is just chess with a twist (familiar openings and opening setups aren't available). Bughouse/Transfer is a completely different game that's based on chess rules and conventions. It's major characteristic is a massive injection of chaos that's quite foreign to the game of chess.
I'd also like to mention that "exactly like normal chess in complexity" is false. How can you say that there are the same number of possible first moves in a standard game versus a fischer random game?
It's obvious that there are going to be exactly the same number of possible first moves plus or minus two. And what that has to do with the perceived complexity of the game, I haven't the slightest.
But you do not know the layout of the board in fischer random. And once you do the number of first moves is not even; the knights could be in the corners...
Bughouse and crazyhouse are significantly more complex games (branching factor over 100 for Crazyhouse, even more for bughouse).