I would say it is just as "safe" as the vast majority of online transactions. Some e-commerce retailers do not store your card or bank account info and this I would say is probably the safest scenario, but the vast majority are like paypal and that information is stored in their database (which can be a security risk, but it greatly simplifies the process).
I have had an issue with Paypal in the past. Somehow my information was compromised and someone used my account to send cash to third person's account. They then used that third person's account to buy "currency" in an online game (which the assumption is they then sold that "currency" to someone for real cash). No idea why the person did not buy game currency directly using my account, but assume there was a reason to do it that way. I tell that story just to point out that Paypal handled it very well and quickly put a hold on my account once notified and had credited my linked credit card within a day.
I do not use bank accounts for transactions using Paypal because I have found their(paypal) dispute process with merchants to be very lacking. If it goes through my credit card though I can use the dispute resolution of the credit card company which seems to be much more consumer friendly. I normally have hundreds of transactions online each year with paypal and both times I had a dispute with the merchant Paypal sided with the merchant, but when I got my credit card company involved they sided with me and resolved the issue.