Ignoring the argument over what gets things accomplished more effectively for the moment. There is a huge difference between their relative foreign policy approaches. In the end, were going to do what we want to do (in an ideal world to advance our aims). How you do that is the big difference.

Obama was a big soft power guy. Europeans like that, as they should. Trump, and to a lesser extent Bush (who at least liked it to look like there was a consensus) were / are hard power guys. Europeans are always going to like the former more than the latter. As much as it might be painful to admit individual European nations are not the equal of the US in anything on a global level. The EU as a whole, sure, but its surely not as cohesive as the US at the moment by any means. Soft power projection gives the appearance of cooperating as equals, even if we're coming in with a plan in mind. Now, obviously pissing off everyone isn't the correct move either.

Not saying I think one is better than the other, but there are obvious reasons Europeans would prefer someone who downplays influence (which is what pissed some Americans off) over one who overtly flouts it.