V10 anon here.
I'm a midlevel associate at a V10 (created this thread: viewtopic.php?f=23&t=193519
) and I have a different take from that of those who have posted so far.
I would advise you to definitely try your best to leverage your second choice's scholarship into a scholarship at your top choice. Your approach is key, however. Instead of seeming gauche or greedy by overtly asking your top choice to match, I would advise you to reach out to HR at your top pick to thank them for their offer and explain that you are very excited about their firm and love <<insert 3 or 4 substantive, insightful, firm-specific things>> about them, but you have an offer of both an SA position and a scholarship of xyz amount from a peer firm. Then ask them a couple of questions that are meant to help you decide which firm to go to. Of course, the point of the e-mail is not these questions but rather to let slip that they have competition for you. If HR gets back to you w/ answers to these questions w/out mentioning your scholarship then leave the topic alone. If, however, they ask for additional details such as the peer firm's name, then provide them the info and they just might match. It is not unusual at all for firms to quietly accommodate associates without disclosing to the rest of the class that xyz person just got a concession worth thousands. Just be careful how you go about it. Let them "surprise" you by offering to match (because, you know, it hadn't occurred to you that they might match when you let slip the info about the peer firm).
By the way, some people in this thread have given you ignorant, catty advice and I suspect it is because you are a URM in an enviable position w/ somewhat unearned money. Be careful who you take advice from in this profession because many law students and lawyers are very jealous, competitive people.