As with ALL styles of engineering, they're HIGHLY transferable from one industry to another. Naturally if you want to specialise, then do the specialisation in the area you're interested in. As a rule, the chemical/oil/gas industry pays well - there are additional hazards which aren't present in an aerospace factory, travel is expected, and the rest, which means salaries are higher.
That said, if you are an aerospace engineer, which is essentially a mechanical engineer with a few more fluids modules, there is NOTHING stopping you working for the chemical/ oil/ gas industry, and being on the same pay as they are. It's just that most people do not do this - they go and work for Boeing, Airbus, aerospace parts manufacturers, where the risks, and hence the pay, aren't as high. The roles you can go into are within reason - An aerospace engineer is not going to be designing microprocessor architectures, and an electrical engineer isn't going to be doing structural analysis for an oil rig, but working in the same industry is entirely possible, and indeed, you'll learn a lot about chemical engineering if you work for a chemical company.
I for instance, work in the aerospace/marine industry, as an electronic engineer, doing nothing to do with electronics, for the majority of the time. I didn't study thermo or fluid dynamics at uni, but I use it in my job all the time - the whole point of studying engineering, is that you learn how to teach yourself. who do I work with? aero eng, yes, but also mech eng, elec eng, physics grads, even nuclear grads. My course mates went into the semiconductor industry, finance (investment banking), communications, mobile telephony, aerospace, oil, and one even went to work for Lidl. on £40k starting. hahaha
Studying chemical engineering because "you get paid the most" is a bit of a red herring. If you want to be paid well, then go into finance, investment banking, or insurance as an engineer, in a non-engineering role. If you can stay there, and make yourself useful (read, irreplaceable), then you can easily be on twice what a chemical engineer working for oil is on. And again, ANY engineering discipline will do for this. Most engineering students realise this around year 3 of their course, so this is an early heads-up.
So in response to the original question - all engineering degrees tend to be useful, and I'd stick with the ones which are the most common - i.e. Chemical, Civil, Mechanical, Electrical & Electronic and Aeronautical. All the others tend to be much more specialised, which is great if you want to be in that specific industry, but that's 3 - 4 years after you first start going to university, where you will discover a lot more about yourself and where you would want to work, and if you know at this stage where you are going to be working, then I'm interested in procuring your crystal ball and using it on the stock market.
Hope this helps,
Stu Haynes MEng MIET MIEEE