The Buck-Strider has a blade thickness of 3/16", or 0.1875".
The Spyderco Lum (Tanto folder, you should specify this) has a thickness of 1/8", or 0.125".
A knife that I remember you have, the SERE 2000, has a blade thickness of 0.14".
There's going to be a big difference in cutting ability just because of the thickness of the Buck-Strider. You could rebevel, but I think that's kind of missing the point of the BS. It's a huge, fat blade for hard work. The blade is just never supposed to break, no matter what kind of hell you drag it through.
Both of them appear to have a hollow upper grind (the grind that's not the edge, I don't know what to call it). The one on the Buck-Strider is not very apparent, the one on the Spyderco looks deeper. I think the Lum would cut much better than the BS, but would be more fragile, if you're going to be using it hard. This might or might not be of importance to you.
Buck's warranty is really good, and you can also fall back on the Strider warranty in the unlikely event that Buck can't/won't fix a broken knife. I've had no experience with Spyderco's warranties, so I can't say how they would deal with a broken blade. I've heard that they can regrind broken tips for you, but I don't know if they charge for this.
Conclusion:
You need to figure out what you're going to be using the knife for. The thickness will make a difference in performance.