I have my human adept set up so I still have a +199% cooldown reduction even when using an M8 Avenger, and I've unlocked up to level 8 with it. Scope plus stabilization mods means I have a rapid fire assault rifle that's nearly as accurate as a sniper.
I have singularity set for shortest cooldowns, and warp for as much damage/cooldown as I can get, and I'm consistently at the top of the leaderboard on bronze/silver. Never beat silver, but got to level 10 a few times, and many times to 8 or so, just couldn't quite finish. Anyways, I play my adept pretty damned aggressively, with warp bombs about every 3-4 seconds, killing one for sure, and damaging nearby enemies that I can finish off with my AR, or even a second warp-bomb to continue the action.
I played a mission with me, two soldiers, and an engineer. The soldiers were near my level. I didn't top the leaderboard that game, but I came in a close second, and the other soldier was a close third. The 4th guy didn't have a great score, but he was doing good work stripping defenses, letting my warp bombs fly even more effectively. So, no, I can't agree that a soldier will always out-kill an adept. I've seen evidence to the contrary.