I know for certain that Cloud, Sephiroth, and Genesis all have the strength to cleave enormous pieces of concrete or steel. We see plenty of this in Advent Children, and I've seen snippets of Crisis Core in AMVs and such. While they'd need weapons possessing strength that's out of this world, it'd also require a phenomenal amount of force from their own bodies and minds. Nothing in FFVIII suggests that SeeD have comparable physical power: Squall & co had to run away from the Black Widow in Dollet (I know it's defeatable, but the default outcome is flight rather than fight); during the G-Garden battle, Squall has to use a barrage of kicks and punches to dislodge the G-Soldier who's sharing a flying platform with him. SOLDIERs are actually strengthened, physically and mentally, by the procedures carried out on them. SeeD, on the other hand, have regular human strength and skill, but augmented solely by energy in the forms of GF and magic.

We also know that SOLDIERs have the strength, reflexes and mental acuity to protect themselves from gunfire, either by deflecting incoming fire with their weapons or by being agile enough to avoid their enemy's aim. FFVIII doesn't provide much basis for comparison - the heroes often encounter gun-weilding opponents, but in the Desert Prison cutscenes they all take cover when facing gunfire.