The GE actually has a significantly higher passive weapon damage bonus (like 10% higher) than the Turian Soldier, because the 10% Geth Weapon damage bonus is multiplicative. For headshots, it's much closer. The TSol's overall weapon DPS will be better because of the Marksman ROF and headshot bonuses and auto-reload*, but from a pure weapon damage standpoint, the TSol isn't that much better than the GE unless you're getting a consistent stream of headshots. When you factor in the additional shield/barrier damage you're doing with Overload and the additional damage of fire explosions, the GE's overall damage might actually be better. But yeah, if you just want to continuously shoot, the TSol is better at that.
With both maxed for weapon damage, the Geth Engineer has 2.5% more weapon damage possible. But since TSol also has debuff and rate of fire increase, he still has more. With the builds posted above, the Geth gets 2 more damage per shot than the TSol, without proxy mine debuff. Factor in extra headshot bonuses from marksman and rate of fire increase (even more than Hunter Mode), coupled with the fact he doesn't need to stop shoot and worry about ramp up, TSol does more damage. But stop me when you've heard this before, TSol does more damage than [insert character here] with [insert weapon here]. It's what he does.
*I have had issues with the ROF bonuses of Marksman when firing some automatic weapons. If I'm continuously firing and activate Marksman, the ROF bonus doesn't apply until I stop firing and then start again. I don't know if this happens with all weapons or only certain weapons, but it definitely happens with some. Normally it's not a big deal, but stopping your firing can really affect your DPS with a ramp-up weapon like the GPSMG.
If you activate marksman first, then start shooting, you'll get both headshot and rof bonuses. When marksman runs out and you're still shooting, you keep the rof bonuses, but lose the headshot bonuses. If you reactivate marksman before you stop shooting, you keep rof bonuses and get headshot bonuses back. So in the case of GSMG, TSol could shoot an entire round with all bonuses intact. Someone can correct me if I'm wrong, but I'm fairly certain that's how those mechanics work.