I don't think it's a matter of aesthetics vs safety, or onsite vs third party (I'm Dutch). Yes, I agree that third-party redirects don't appeal to many users, but the same goes for a payment form hosted on your site. You have to understand that the credit card is a relatively new form of payment, where in the US almost everybody has one. If we order something online, we usually pay afterr we've received the shipment, or through a system called Ideal (in The Netherlands, that is. Can't vouch for other countries), which is basically some sort of API between the website and your own bank. Paypal isn't used much by European websites, other than the ones targetting the whole world and some shifty websites. fYI: most webshop CMS like Magento come with a built in Ideal shopping cart.

The problem is that, while one economic region, Europe is still a collection of separate countries. We all have our own banks, so the chances of one European payment provider coming are slim to say the least. What I would like to see is a universal payment provider with the same reputation as a regular, trustworthy bank.

So to answer your question: it doesn't really matter if the solution is onsite or third party, as long as it's trustworthy.