I do not own an Omega, but I will tell you why they are appealing.
Their quality, IMHO, is on par with Rolex at a fraction of the price.
Rolex, no doubt, is my favorite, but when you look objectively at Omega vs Rolex, it's very difficult to justify the prices Rolex charges when compared to Omega.
With better marketing in the past 40 years and a little luck, Omega could easily be the brand we were tauting as Number 1 and Rolex a bit behind.
For evidence, I cite the moon landing as a prime example. In terms of the adventure/pioneer spirit, was there any better achievement in the 20th century?
Rolex got me (and millions of others) to identify it with the explorer, the adventurer, the world traveler, the diver, the CEO etc. . . How? Through unbelievably successful advertising. I would flip through a National Geographic and see the ads for the GMT. "If I had that watch, I could go places!" I turned the magazine page and saw the Submariner. "If I had that watch, I could find buried treasure."
I don't remember seeing a single ad for Omega. So, I believe, the escalation of Rolex over Omega had little to do with quality and everything to do with marketing.
Sure, many will mention the inventive nature of Rolex--the Pan Am pilots request for the GMT and the first waterproof watch--to counter this argument. But honestly, is there any more impressive achievement than being the only watch ever worn on the moon?
Always found it a bit sad that Omega failed to capitalize on this fact and now takes second place when compared to Rolex. But perception is everything.