Those aren't exactly the best class/weapon combos. There's nothing wrong with them, they're just not going to bring in amazing results. The Mantis is actually pretty good, since it's light, powerful and easily to get up to rank X, but it works best on a more caster-y character (power -> shoot -> power -> reload -> repeat).
If you want effectiveness, I've found that a Human Sentinel spec'd for rapid detonations is the most serviceable of the initial human classes. Beyond that, of the initial set of unlockable classes, Asari Adepts are still good and so are melee Krogan on bronze. Turians are decent, but want certain guns to make the most of their stability.
I do use a Human Sentinel specialized for detonations. It is quite effective. I've always liked the Krogan Sentinel, but I can't get the Soldier to work. As for Turians, I have a Soldier and a Sentinel, both with Phaestons. Both worked well last time I used them but then, so did the Mattock-using Human Soldier.
Originally Posted by Psyren
What level is your Scimitar? That's a caster shotgun - I would try to get a stronger one if possible. Depending on the level, Katana X may actually pack more punch, and you shouldn't have to worry about weight on a Krogan Soldier.
I would consider dropping one of those weapons altogether for an assault rifle as well, if you have a good one. The Krogans' strength lies in their durability, allowing you to hang out of cover longer and pump sustained fire into enemies from fairly close without dying. So a Phaeston, Revenant, even a Mattock/Sabre might be a better option if available.
Right, I forgot to mention - I equipped a Revenant with the Omni-Blade upgrade on him instead of the Scimitar. I haven't had the occasion to try it out yet, though.