The schools are so close in ranking I think it really comes down to geography. I think Harvard has a slight edge in prestige, clerkship placement, and academia. If you just want to do biglaw you can get those jobs at either. The class size is super small at Stanford and it is supposed to be a more relaxed atmosphere. The drawbacks of that are less class variety and lots of gossip. Harvard, on other other hand, is huge with lots of niches to fall into but possibly more competitive.
Congrats.