I don't think lack of heart is necessarily it's problem; John C. Reilly probably gives it more than most monster movies of its type manage even while being the comic relief, and while what Samuel L. Jackson is doing isn't "heart" in the traditional sense, the decision to go the Heart of Darkness/Apocalypse Now route rather than the go for the traditional pulp-adventure atmosphere is a good one and Jackson makes it work.  I kind of admire it not going the traditional route in that way; I don't think you're going to beat Jackson's for that sort of "heart".

(And, yeah, I'd put Peter Jackson's as the best in that category; the expanded runtime and historical perspective give Naomi Watts and Jack Black the chance to do more with their characters than the originators could.)

The knowledge that this is going to be part of some Legendary kaijuverse makes it a weird one for me to approach.  I enjoyed it a great deal - the effects and action are great, better than most monster-battle movies at showing massive power, evenly-matched fights, and humans actually managing to be a non-trivial part of the action - and the characters grew on me enough that I was actually a little disappointed to realize that they likely wouldn't be able to show up in the inevitable Godzilla vs King Kong movie because of the 40-year gap, and the waste that represented for the franchise dinged it a bit for me.  Unfair, in some ways,but not in others, if we recognize this as a part of a whole and judge it based on its contribution to that whole.