I'm in the "why chose?" camp. They are both great mid level watches that deliver on their promise. Taking marketing and supply/demand issues aside and just evaluating the actual watches, to me, Rolex may come ahead by a slight margin.
Omega is defiantly a bolder, younger and more innovating spirit. But that does come sometimes with a very SWATCH like tendency to fall into the gimmicks or LE after LE, unnecessary innovations the lead to hasty design choices sometimes, and a somewhat unfocused production. In other words, sometimes it looses a little on identity and cache for the sake of pushing things through. There is such a thing as "if it aint broke don't fix it" Did the PO, which was perfect on the 2500 series, (LMLE anyone?) needed an 8500 movement that changed it from a bespoke but present tool icon into an overstated hockey pug sized monster? Did the AT need to change to horizontal when it was perfect? do we need an everlasting amount of heritage and fake patina limited editions? How many sides of the moon are there? etc. Quality is there and it remains an amazing brand but it's somewhat diluted. Fortunatelly they have kept the Moonwatch pure. When you are one part of a very large machine marketing and production choices are made on sales targets and bottom lines more often than not, which perhaps makes it unavoidable to be so quick to produce, change and create new offerings.
Rolex, not belonging to a larger house, has the choice to remain brand-centered. One of the reasons some of their watches have become so iconic and valuable is precisely because they remain virtually the same for decades with minor changes (that are tracked very carefully by their fandom) Just as Omega does not change their moon watch much (and everyone respects and loves that) Rolex does not change their more successful lines either. It's just that Rolex has more iconic models than Omega. That being said they have made some interesting changes (some questionable and inconsistent) during the last decade.
The larger-then smaller Explorer case with the metal-then lured numerals, The maxi cases of the ceramic subs and now the 41 mm finer proportioned cases. The 39 mm Op changed fast into the 41 mm "Stella 2" OP, The 41 mm DJ, The ceramic Daytonas with a return to black bezel from metallic. (A change that is not small considering the iconic status of the watch). And then there are changes to the movements as well. Albeit of smaller degree than the Omega quest for co-axial perfection.
To this extent the more conservative Rolex has made changes that are relevant to the fans and aficionados but not so much to the public who perceives them as "the one" unchanged iconic watch. It is not true.
So is Rolex less bold, more boring, more conservative than Omega as a brand? Yes. Is it also more reliable and recognizable in its design and identity?, yes. Is Rolex superior in quality? No, I think they are both great quality at the top of the mid level luxury watch market. They are both great and both deserve their recognition and status.
Add to the Marketing and Sales strategies and, of course, Omega is an attainable brand that respects their customer and the rules of commercial enterprise and Rolex is a freaking circus that either allows themselves to be hijacked and ransomed as a brand, or looks the other way, or just shrugs their shoulders as if their job it to make the watches but not to sell them....that is a job for the "mercs" of horology around the world.
This makes, to many, Rolex owners suspicious of dealings or grandstanding or boasting because.... "Look, I got not one but two!! and you got none!" It is unfortunate because some of us just like the watches.
I reckon if it wasn't because of the inflated circus around Rolex, if it was just on the merit of design, metal and craftsmanship; Most omega fans would have little room for comparisons and competitions....they would embrace both brands as equally worthy with different temperaments.