Since the TSX bullet is copper with no core, it will be longer than a bullet with a lead core. The Speer bear claw bullets do have a lot of copper (solid copper base) with a little lead in the forward part of the bullet. The 120 Spitzer is a hot core bullet that would have a lead core. Bullet accuracy would depend on individual rifles. They all seem to like some thing different.
Hot Core Speer bullets (a bonded bullet) hold together well and should perform OK on big game animals as the Barnes TSX should. I think it comes down to which one shoots the best in your rifle.