You can have my two-wheeled bag when you pry it from my cold, dead fingers. Partially-recessed wheels are virtually impossible to break no matter how much I abuse it--or if I buy a bunch of beer and have to check it. They take up less space, roll more smoothly (especially on rough surfaces), and are far more stable when overloaded or used as a base to stack other stuff on. I regularly put my kid's bag in his car seat and strap that to the handle of my two-wheeled rollaboard.

Spinners are easier to push in a crowded airport vs. two-wheeled bags that are awkward to push in front and impossible to push alongside. But I spend so much time walking around hotels, city streets, parking lots, etc. that it's not worth the tradeoff.

The Travelpro FlightCrew series (not to be confused with simply "Crew") are still available as two-wheelers. Mine is 13 years old and still kicking. They're quite cheap (sub-$200) for the durability you get; they are heavy though, so if you have to carry it up lots of stairs or often fly airlines that weigh cabin baggage it may not be the best option.