I own a ton of models from both companies, so I'll take a whack at this....
Strength: Many of Spyderco's models emphasize light weight; many of the most popular models have FRN (fiber reinforced nylon) handles without metal liners. There are some lightweight Benchmades, like the Griptilians or the carbon-fiber gents folders like the 770; but most are solid slabs of steel, titanium, G10 and/or aluminum. So overall, I think the average Benchie is stronger than the average Spydie; however, neither are in any way flimsy! I know folks who've beat the crap outta the same Spyderco Delica Lightweight for over ten years, with no damage. Whichever you pick, unless you lose it, it'll outlast YOU.
Sharpness: My experience is like that of others: never seen a dull Spyderco out of the box, while Benchmade occasionally ships one that could use a little edge work. Personally, I don't think it matters; unless it spends it's life in the box, ANY knife that's used will get dull, and need to be sharpened; it doesn't matter to me if the first trip to the stone is right outta the box.
Long Last: See above. Unless you try to use one for felling timber, either a Benchmade or Spyderco should outlast you.
Appearance: That's a matter of taste. I personally think Benchmade's designs are more elegant, with a more "classic" appearance; Spyderco tends to go for the "form follows function" school of design. But, hey, knives are tools; function *should* be important, right?
What They Can Withstand: Most Spydercos are lockbacks (although Spyderco does the tightest, strongest, most reliable lockbacks out there), along with some liner locks, and a few models with their rather remarkable Compression Lock; Benchmade has a few nicely done frame locks, some liner locks, but most of their line is based on what IMO is the best lock out there, the Axis Lock. ANY knife will break if you abuse it; but both Benchmade and Spyderco build some seriously tough folders. Within reason, I think it's safe to say that either a Benchmade Skirmish or Spyderco Manix (just to pick two of the beefier from each line) can take anything you can dish out.
Warranty: I've never had a warranty issue with any of mine, so it's hard for me to say. Both have excellent reputations.
Company and Service: Again, I haven't had any need to try out the service side of either business. Both of their reputations are excellent, however.
Honestly, you can't really go wrong with either company. Both have wide enough product lines, thhat you should be able to find something you like. Buy one of each, and be happy!!