It depends WHY you want to get into engineering. Seriously.
If you're doing it because you like the cool stuff then it doesn't matter which branch you pick: if you're doing something you enjoy then you're not actually working.
If you're doing it for money then, apart from hiring a hitman to take out anyone whose reputation looks like rivalling yours - thus making you top dog and able to command your own salary, you're not going to get far.
I'd go for cosmic's answer: a good background in mechanical engineering will at least let you work for different companies on vastly different products (although, truthfully, the majority of day-to-day engineering jobs don't have much "cool factor" attached to them
1).
1 I mean, how many fabulously sexy groupies am I going to get if I make public that my "finest hour" professionally is probably this and its cousins?

Yeah, I had a few offers to go work on nuclear weapons, but despite it being
much cooler, you tend to get officious little (correction: official very large) men making polite requests that you don't use it as a chat up line.
Life sucks all round.