Both folders fit my hands well, and I'm assuming if you're asking this question they both fit your hands well, too. If you haven't taken them both for a quick test drive, be sure to do so. A few people don't like either the Starmate or Axis, just because their hands didn't fit well on one or the other.
Other than that, the main differences to me come down to: the lock, and the edge.
The lock: I don't buy liner locks anymore. However, I'd say Spyderco's liner locks are particularly good, so if I was in love with the Starmate, in this particular case I would probably buy it anyway. The Axis lock remains in another league, in my opinion. It is astoundingly strong, and just as reliable. The Axis is the winner here (for me), but the Starmate still makes it above the "cut line" for consideration.
The edge: Spyderco understands edges, plain and simple. The Starmate comes with a thin, high-performance hollow grind right from the box. The Axis comes with Benchmade's typical thick-but-strong sabre grind, with an edge that won't perform as well as the Starmate's out of the box. Since the edge is something you'll be modifying anyway, you can always thin your Axis's edge down if you decide you want a thinner, high-performing edge. Just keep in mind you'll have to work at reprofiling the edge a bit if that's what you want. Winner here is easily the Starmate, but the Axis's edge can be brought up to the par with some reprofiling.
The last thing to think about is the steel. Many people rave about 440V, but some folks, like Cliff Stamp and Outlaw Dogboy, have exposed some areas where 440V isn't the best choice. It's worth trying to find those posts and reading about it.
All in all, hard to imagine going wrong with either knife. Both get consistently good reviews.