I'm going to Latham next summer. I didn't look into Skadden because they didn't have the location I wanted, but I have talked at length with a guy I know who spent last summer at Skadden and I've also done the same w/ a guy who spent last summer at Latham. They both raved about their firms and both are returning as associates next year. As you know, the two firms are very similar in many respects (namely they are HUGE V10 firms). The compensation, QOL, work, prestige, exit options, etc. are going to be very similar for both. I would say pick the one where you liked the people the most (which probably doesn't help much).
FWIW, after doing my callback w/ Latham and getting an offer I cancelled a callback at a V5 firm and turned down my other offers because I knew Latham was where I wanted to be. Everyone I met there was really friendly/personable and from everything I've read it seems like Latham is probably the best bet as far as overall job satisfication goes for a V10 firm. Also, for me a very big draw was the 2-year unassigned program. I know at the Latham office I'm going to they had 15 SAs this past summer and a number of them split with other firms. They extended offers to all 15 and all 15 have accepted. To me that says a lot. Good luck w/ your decision.