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I applied to three T10 law schools yesterday. After I submitted I took a fresh look at my personal statement, moved some things around to make it read better and wrote a new and considerably stronger conclusion. The revised personal statement is substantially better than the previous version I submitted yesterday. I'm wondering if it is worth it to resubmit the new personal statement? I fully understand that they are going to read the new version alongside the old one and that it probably looks bad, but I think the one I wrote today gives a much clearer explanation to why I want to go to law school. Has anyone had any experience with this before? Any advice would be greatly appreciated.

I wouldn't. I think they would say "well, you should have thought of that before" and I think it would draw negative attention to what is probably a good essay to begin with. Many people on these forums have said that personal statements likely won't make or break you. Since you only moved things around and didn't correct any glaring mistakes, I'd let it go and use your improved essay for future schools. As I'm doing these apps, I'm improving things with each app. It's practice makes perfect. But it doesn't mean I should try to go back and make law schools accept changes to past apps. Good luck!