> In Bohm's theory there is no collapse of the wave.
No collapse of the wave-function takes place upon measurement. One must obtain, nevertheless, the "reduced" wave-function of the system. Once a specific result has been obtained in a measurement, only that term (of the global, universal superposition) counts. This is a sort of "effective" or, better, "pragmatic" collapse.
OK, although in principle the collapse could be considered as non effective, because if you "erase" the information you get from the measurement, in principle you can re-establish the interferences (quantum erasing has been tested experimentally, but of course not by an observer on hims/herself).
> So it is indeed as deterministic as Everett formulation of QM.
Are they both non-local, at least in principle? I'm asking this because, usually, I read that MWI is local, and that seems to me very very strange, just because of the "split". I also read that the Bohmian theory is non-local (though this original non-locality is almost, but not entirely, suppressed by the general quantum "equilibrium" condition).
Bohm is admittedly non local, and indeed Bohm's proposal is somewhat difficult to sustain in the relativistic frame (of course some people makes try ...). Everett is local, as he realized himself, and this has been very well explained by Deutsch. Basically there is no splitting but differentiation. See also http://www.hedweb.com/everett/everett.htm#local for argument in favor of locality by a "splitter". Now "locality" is a tricky word, and I can find sens to it such that Everett and comp are highly NON local from the first person point of view (like comp indeed).