Is it considered unprofessional to use an outside payment provider instead of your own branded solution?
I use Amazon's web services to host customer data, and there is a limit to the exclusivity you can provide. So either I need to rethink my hosting situation or use DevPay, which would remove the problem. But I am concerned about appearing inexperienced by having to redirect off to Amazon or PayPal to handle credit card processing.
It really depends on your industry and what is considered appropriate.
You might want to take a look at the three leaders in your market, see how they process payments and take your cue from them.
Another prudent idea is to ask your top customers what type of payment setup appeals to them and take that into consideration when making your decision.