Randomness gives a better simulation. You can't predict everything. But less randomness gives a better strategy game. For me, games are about interesting choices, and while risk managment can be interesting, there are better mechanics. (Random rewards "feeling" better is an argument
against randomness for me. I don't play EA to interact with a Skinner box.)
As JTG said assault resolution dice offs and strategy rolls can be problematic. My solution would be to toss out resolution roll off entirely (which, if you remember the discussion we had about that a few months ago shouldn't surprise you

). I see a couple of solutions to the strategy roll. First one would be to let higher SR choose who wins strategy in the first turn, and then alternate (not alternate who goes first, but who chooses who goes first). It makes teleporting safer, which is mostly a concern between armies with equal or close SR (other situations, like Marines losing their terminators because they rolled a 1 and the Nids rolled a 5, are effects I'm happy to get rid of). It would also make very low SR better (because you only care about if you're lower, not by how much), while making high SR slightly worse (but that's offset by letting you guarantee the first move in the important third turn).
Just leaving it in is a better option than for assault resolution, but it gives a higher benefit to having a high SR than plain rolling does.