As you have noted, the Drake is a two piece, available with round or elongated bowl and also available in an ADA-height model. As for flushability, the Drake gets the highest marks in terms of the number of grams of "material" it can successfully flush. The Drake has the G-Max flush, as does the Ultramax.
The Ultramax appears to be popular due to the G-Max flush and the one-piece design. The advantage to the one piece is that they are somewhat quieter and they are much easier to clean as there is no space whatsoever between tank and bowl, and therefore no space for bacteria, etc., to hide.
The Ultimate is also a one-piece but uses a Power Gravity flush and, according to Terry Love, is a good toilet. It is less expensive than the Ultramax, I assume due to it not having G-Max. Because of that, it doesn't have the "gram flushability" that the Drake and Ultramax have.
Personally, I would go with the Ultramax because I like the one-piece and it seems that you could flush a small animal down it with no plugging issues. Same goes for the Drake. With children, I think it would be worth the extra expense to choose a G-Max model. As for choosing between the two, the issue is one- or two-piece and that's strictly a matter of preference and budget.