The 8500 gives me everything I need for a travel watch, because it has a time-zone jumping hour hand feature instead of a quick set date. I rarely travel outside of the continental US, but if I travel from Chicago to NYC it’s so easy to adjust the hour hand one hour forward while the minutes and seconds hands continue to run. Of course you don’t have the ability to read both Chicago and NYC time on the watch, but it’s easy enough to do the math in your head. And there are plenty of 8500 watches in sizes like 38mm that wear well on my 6.5ish inch wrist.
The AT GMTs were released in 2012 on the 8605, which is based on the 8500. So you still have the time zone jumping hour hand instead of a quick set date but you also get a GMT hand to enable you to keep track of time in two zones and all hands (including GMT) can be set simultaneously with hacking when the crown is in its farthest position. The watch came in 11 models with various colors, materials, and bands, but all were 43mm case diameter and about 14.5mm tall. So a big watch.
The PO GMT 8605 came in four models, plus some “good planet” options, all at 43.5mm and crazy tall, like 17mm. Same 8605 as the AT GMT but with a bi-directional rotating bezel that enables you to track 3 time zones. The newer PO GMTs are metas watches using the upgraded 8906, which operates similar to the 8605 but better certification and likely a higher price in the pre-owned market— plus they are still huge, either at 43.5 or 45.5.
There is no longer a Deville GMT in the current omega catalog. My guess is that if you bought one pre owned it would be an older watch that probably had never been serviced and would need to be.
If I started to do more international travel I might buy a GMT, because they are fun and useful, but I would want something at least as current as the 2012 AT GMT (there was also an AT GMT with a chronograph in 12 models that IMO was a monstrosity of a watch). Honestly I would probably look for a GMT from a non Omega brand since all the Omega GMTs since 2012 have been at least 43mm wide and 14mm tall and that’s just too much watch for my wrist.