Ok, well the title says First Class SOLDIER vs. SeeD. If I remember correctly, in Crisis Core they explicitly say that the only first classes are Sephiroth, Angeal, Genesis, and eventually Zack. So, we have 4 elite SOLDIERs there who are infused with mako and have materia, while in FFVIII you have the top of the SeeDs which are basically all the main party (Squall, Zell, Selphie, Irvine, Quistis, etc.) who have the power of the GFs who make them immensely stronger. I believe the SeeD have it. I believe that it would be a great fight, but regardless of how you match them up, I think the SeeD would come out on top.

Also, I am not sure if this was meant to be just a one on one battle or all of the forces combined, but either way I say the SeeD will be victorious.