I just returned from my third Overseas Adventure Travel (OAT) tour, this one "Crossroads of the Adriatic" through countries of the former Yugoslavia, and I like them a lot. I think they offer what your message describes. Group size maximum 16 on most tours, free single supplement readily available also on most. Impressions of the others you mention, with caveat that I have not myself traveled with them:
Gate 1: I saw something of their operations as their groups were frequently in the same hotels as our OAT, and their guides (as ours did) posted daily itineraries on the bulletin board, which were fun to compare. As stated by other commenters, their groups are larger, often at least twice the size of OAT. Gate 1 groups tend to have more of a mix of travelers from different countries, for better or worse. OAT focuses on the U.S. market and virtually all OAT travelers are Americans. The equivalent Balkan Gate 1 tours seemed to be a bit faster paced (less time in each city) and have relatively more "optional" (i.e., extra charge) activities than OAT, compared to those included in the tour price (which of course you can skip if you want, but have paid for, so most don't). The guides seemed equivalent -- ours was great, but they are independent contractors who often work with different companies, so she had done Gate 1 tours also, and knew the ones doing the Gate 1 tours we encountered. But obviously you'll get more personalized attention from your guide in a group of 16 than in one of 40.
National Geographic: With "name brand" tours like these (or Smithsonian, college alumni affiliation, etc.) I think you pay a LOT for that brand name. I've seen the Nat Geo brochures for Egypt, for example, which I did with OAT, and it looked like they charge at least twice as much for what appears to be more or less the same thing in every important respect (accommodations, tour length, activities). These brand name tours seem often to have a U.S. expert (such as a college professor) accompanying the group in addition to local guide, but frankly, there has never been a time on any of my OAT tours that I felt that I would have needed or wanted to be guided by a U.S. professor instead of, or in addition to our incredibly knowledgeable in-country guides, or had any desire to pay extra for that.