However, just to contextualize my comments. My own background is a bit different, I'm already a bicultural/bilingual American as I was born and have lived during my formative years in the "motherland". I've studied 3 languages in addition to English and my mothertongue. I've also travelled/ lived abroad in Europe (Spain), Latin American (Peru and Mexico) and Asia. I live in a huge tourist attraction city (Washington, DC)
And I've encountered a lot of tourists, backpackers, US military stationed abroad, and expats of Asian, European, and American/Canadian background. It's admirable that Europeans are multilingual but as EffEm pointed out that's also partly due to geographical proximity and necessity. I think mentally there would be more of a comfort level.
The short answer:
From my personal observation, there is not much difference between an American and a European tourist *outside* of an European or American context.
The long answer:
Obnoxious tourists also rub me the wrong way, but honestly I think part of this is just 'groupthink' and the fact when people are in different countries/cultural contexts - they just don't care about people outside their group. And how comfortable people are outside the familiar.
I have to disagree that it's only Americans who are gauche or inconsiderate in this way. I don't disagree that Americans are rude and don't try hard enough in your book, since you are speaking from the perspective of a 'native' and insider. I would imagine that European tourists in general feel more a part of and invested in getting along with 'the natives' especially if they're part of the EU.
However as a 3rd party outsider, when I was travelling in Europe and Latin America, tour groups and small groups of other Europeans were really...basically they stuck out. People in tour groups or their own small groups are not particularly friendly and are generally stand-offish if not downright rude and demanding. They are kinda like roaming groups of bulls in a chinashop. I saw some behavior that was almost comical and some that was downright racist. And in the south of Spain in Andalucia, lots of British expats party and even live in Spain without learning more than survival Spanish words - on par with Americans I think.
Travelling through really 'underdeveloped' parts of Peru I met many backpackers/tourists of European extraction who barely spoke or did not speak Spanish or Portuguese who were trekking through Latin America. It's quite common. In general there's an attitude that they are better than the natives - you might say I'm judgmental or paranoid but if it this attitude is 'subtle' it eventually comes out blatantly.
Trying to tie this in a little to the OP etc., language and whether you bother to learn the 'native language' is significant only as much as it reflects your larger attitude and level of respect for 'the natives'.
In general, the attitude of the tourists from the developed world (US/Europe) was similar across the board regardless of their native tongue. In general, I cringe and I try to stay away from (other) tourists. Especially when I see a group of mostly middle aged to older ambiguously European tourists. Or groups of early 20 something backpackers looking to party. Even in DC (which is a huge tourist draw) groups of tourists need to be avoided as they do the 'groupthink' thing and take up LOTS of space and basically get in your way. I think part of that is almost inevitable for a tour group regardless of location in the world.
Basically - I think it is possible to be a respectful tourist, but I think this has more to do with an individual person's actual desire, awareness, and level of respect for people who are different from them.