It depends on what you want to learn. Do you want to learn lots of white-people history? Is it very important to you to be in developed countries, where you can probably count on having all the amenities you're accustomed to in the US? If so, one of the European tours would be preferable.
But, if you'd like to learn about non-white indigenous people, or learn about how groups of white people have really screwed things up--not that you wouldn't learn this in Europe, but it's different here in Latin America--and it's not that important to you to be assured of electricity, hot running water, and flush toilets everywhere you go, then you might find the Latin American tour more interesting.
On either continent you can find historical sites that are many centuries old. Both have cathedrals, though certainly there's a statute of limitations on how old the cathedrals built by Europeans in Latin America can be. I don't know of many Mayan, Incan or Aztec pyramids in Europe, though.
Oh, also... if you absolutely hate changing money, go to Europe. Except for the UK, which uses the pound, the rest of the European Union uses the Euro (AFAIK
). You could change money twice (once for London, and once for your other destinations) and not have to do it again. This is not the case in Latin America, though depending on the US dollar's strength when you go, you may be able to pay for some things on the street with US dollars. Each country has its own currency, it seems. Barring a local-economy crash, you're best paying with the local currency.
You will meet wonderful, giving people wherever you go. You may also encounter mean, nasty people wherever you go. Any time you're in a touristy area, the risk of pickpocketing and purse-snatching goes up. I've been warned many times by locals here in Bolivia not to wear shiny jewelry since that can make me a target--no one warned me about this in Spain, so I wore my gold kartoush out and about in the subways and on the streets.