Its funny that you mention the historical aspect of the trips, because I intentionally stayed away from Europe trips (including the ABDs) for several years because they were so heavy on history and we did the ones with more outdoor activities instead. I know my DS is not interested in history he likes rafting, ziplining, etc. and animals. But when we finally did a European trip he loved it. There were a lot of activities in addition to the historical tours, but even the historical tours were fun for the kids. The local tour guides made it entertaining for them.
I havent done the Italy trip with either company, so I cant speak to that. The first TB trip we took in 2010 was the Northern CA/Yosemite trip. It included kayaking, biking, visiting the Monterrey Bay Aquarium, etc., a lot of activities that were fun for everybody. The kids did rock wall climbing and a junior ranger activity at Yosemite and the guide came up with games and contests (with prizes) for the kids throughout the trip. Last year we did the Danube cruise, which I remember in more detail since less time has passed. There was a scavenger hunt for the kids in Bratislava, a bike ride into one of the small villages for ice cream, a visit to the Vienna Prater where the tour directors challenged the kids to a bumper car battle and rode other rides with them, as well. They had a race with prizes through the maze at Schonbrunn Palace. They baked and decorated cookies. There were contests of some sort every day where the tour guides gave play money as prizes and the kids could use it to buy things at the gift shop. The tour directors purchased and assembled kites for the kids to fly on the deck of the boat, which was really cool. They had a dance party with refreshments on deck for the kids (no adults allowed except the tour directors), which gave the adults a chance to have a quiet dinner or a visit to the spa. We had an activity near the end of the trip where everybody made a sculpture of a face out of marzipan. The guides took all of the kids sculptures (and there were probably 40 or more kids) and made up a funny, personalized award to present to each kid along with a prize. They bought a lot of stuff for prizes and everything that was left over, the kids bought with the remainder of their play money. Im probably forgetting some things, because there were so many extra things the tour directors did for the kids. But aside from the surprises, all of the activities that werent geared specifically toward the kids were still a lot of fun for them. Ive been on 4
ABD (#5 booked for next summer) and 2 TB trips and my experience has been that TB has as many kid friendly activities as ABD. I will definitely be taking more TB trips in the future, as well.