Is it considered unprofessional to use an outside payment provider instead of your own branded solution?
I run a web service where customers pay a monthly fee. Right now it is running through a payment gateway where the customers provide their billing information once on my website, which is then automatically submitted to the provider to set up recurring billing. The upside of this is consistency: Users see only my website and are not redirected to a third party.
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.