the two courses are very different, being science vs engineering, so all the usual "understanding vs applying" arguments apply.

Firstly in terms of difficulty and respect garnered I would have to rank physics the highest of all subjects. There will be tons of maths involved and you will learn all about the underlying forces of the universe. Quantum mechanics, relativity, particle physics and atomic structure etc are these things that interest you?

If you find yourself reading articles in say new scientist about antimatter and the Higg's boson then that's going to be an indication about which one to choose, as physics is all about exploring and trying to understand these concepts and theories. With the exception of thermodynamics I don't think you will go too deep into natural laws with mechanical engineering.

On the other hand mechanical engineering is highly employable because it's so useful. If you're more interested in building machines/cars etc (doing and enjoying this stuff in the past is pointer) then I'm sure it's highly rewarding. I would also argue that you're more likely to make a measurable impact in this field, as much of front line physics is so mathematical and conceptually impossible, or expensive ie CERN.

So having a good degree in ME will pretty much guarantee you instant employment because it's in such demand. However I would think physics graduates earn just as much and probably more, because they can walk into many different jobs. It's just that getting a direct job in physics is quite hard.

So really you should do it based on what you've found most interesting so far in life. They are both good degrees, it's just that in my opinion physics will open your mind more, although as I said don't be too surprised to not find yourself working in that field later on if you do choose it.