There are huge differences between European countries but by and large I think the answer is indeed that (parliamentary) leaders (I am using the term loosely, the person leading a party into the election isn't necessarily the leader of the legislative or of the party's parliamentary group) have greater standing in their political party than American presidential candidates.
And the reason for that is a little bit backwards: It is very difficult to position yourself to be the country's leader or even achieve any significant electoral success without taking control of a party. It's slowly changing (e.g. in France) but there is usually nothing like the US primary process, the only way to be regarded as a viable candidate is to take control of a major party's leadership well in advance. That process isn't necessarily very open or democratic and will at most involve card-carrying party members (if it's not restricted to the party's members of parliament or governing bodies) so you need to have a deep network in the party to succeed.
Without pushing the comparison too far, when you see something even remotely similar to Donald Trump (namely someone who is, in some way, perceived as an outsider and manages to circumvent established party power structures to make a large impact on politics and/or participate in government) then that person usually needs to create her own political party just to stand for election (Pim Fortuyn, Ronald Schill, Geert Wilders, Bepe Grillo…) or to take control of a fledging party which can be used to challenge the other parties (Christoph Blocher). That party can be an empty shell but the leader will, by design, control it entirely.
Incidentally, when you are not voting for a president but for a parliament, the name of the leader (and presumptive prime minister or head of government) might not even be on the ballot (often, he or she must run in only one district, typically a safe one). Interestingly, even when voters ostensibly have to choose between lists or parties, there is sometimes a tendency for elections to become more “personalized” through the attention devoted by the media to the main figure in each party and some commentators have complained about that (e.g. in Germany).