This is a difficult question to answer - mostly because 'rewarding' is such a subjective thing. Personally, I find cleaning my garage and tinkering to be 'rewarding' - but the salary options for people paying you to clean your own garage are slim.
about this first:
are your goals in life? What do you aim to accomplish?**
Pile of Money
If your goal is exclusively to make a pile of money, pick Chemical Engineering
Biomedical Engineer Average Salary - $86,220/year
Chemical Engineer Average Salary - $97,360/year
Source: The US Labor and Statistics Page - http://www.bls.gov/ooh/architecture-and-engineering/home.htm
of Available Jobs
Chemical Engineering - 34,300
Biomedical Engineering - 22,100
The stats back up what I suspected - there are more jobs for Chemical engineers than Biomedical engineers - and Chemical are paid better. Now to the last part of your question "respectable". Who are you trying to impress? Academia? Other Engineers? Medical professionals? The answer to the question will depend on 'what do you want to do?' I can't answer what will look more impressive - because I don't know what your target audience is.... perhaps you should consider the question below:
drives your interest?
Chemical engineers will probably be more 'industrial' in nature. You will be manufacturing chemicals, working in the petroleum industry, or find a small niche in some other manufacturing/industrial area. Biomedical engineers work on 'medical' or 'bio-medical' applications - equipment used by laboratories and hospitals. Perhaps implants. If you want to have a specifically 'medical' slant to your engineering, then go biomedical. However - most biomedical engineers straight out of college might have trouble finding a job in any industry OTHER than medical. Less jobs means more competition among people (although - if you believe the media - there is a 'shortage' of engineers, I'm reserving my judgement on that issue). A Chemical engineer will probably be easier to move across various disciplines and companies where a biomedical engineer is specifically medical/biology. (My personal experience - I have worked in manufacturing and have had collegues with 'Chemical Engineering' degrees. I have never worked in medical manufacturing - and thus have never meet a bioengineering major). I wanted to do bioengineering when I was in graduate school - but the limitation of available work at the time caused me to remain a more generic 'electrical & computer engineer'.
There comes a point in life where it doesn't matter how much you make - it matters how quickly the day ends. If you work on fun things at your job and love the people you work with - you will be surprised how quickly the day ends. If you make a large pile of money, but hate what you do - days drag on and on. The happiest people on the planet are those that love what they do and make a decent salary. You have already chosen 2 of the higher end paying engineering disciplines - just make sure that you are choosing them because you will LOVE the topics - not because you LOVE the money.