I think you've answered your own question - go to Imperial! :P Also thanks for reminding me that Imperial has other cool options like computational finance (I just remembered that that was a big appeal of that course). Imperial is more reputable, it teaches you theory from the ground up and also do cool projects which allows you to work on your practical skills as well.
If you've done aero eng I honestly don't think you'd have problems rapidly equipping yourself with practical skills in the future, so the courses at Imperial sounds a lot more relevant. The UCL course doesn't require ANY prior experience right? I'd put a lot more trust into the Imperial one which has stricter technical requirements, I think you'd learn more that way. (I'm not trying to convince you to do either, but rather speaking out my own thoughts as I have the same problem as you - I did physics at Imperial and I've done some ML MOOCs.)
This might be a bit less relevant - there is a big hype around Kaggle competitions but the opinions amongst experienced people are mixed e.g.
https://www.quora.com/How-do-I-get-a-job-as-a-data-scientist-if-I-have-no-prior-experience-as-a-data-scientist/answer/Brian-Farley-3?srid=seh5 (I find Quora to be a great source of info on personal experiences. They also have great answers about how people found the UCL ML course, couldn't find anything about the Imperial one though.)
Oh also if you're interested there's a GREAT course on data science called CS109 - it's rapidly paced and extremely hands on, and I imagine this might be what the UCL course might be like. But see, these days it's so easy to do hands on stuff by learning it online!
I've read somewhere that CSML starts 2 weeks earlier than the ML course to take extra stats lessons, but I'm not sure if that's still true. I've also read that people have in the past switched between the two, and also that you'd have to sacrifice some of the ML courses in order to take stats ones which isn't necessarily a good thing.
I'd draw up a massive list of pros and cons of UCL/Imperial and assign points to each criteria and add them up. :P