I've pondered this thread for a couple of days, having been fortunate enough to own a number of watches from each of the three brands.
I think I've ended up of the opinion that trying to rank the brands in order is almost pointless, whilst in many respects they are in direct competition and sit in a similar position in the watch market, we as WIS focus on such minute detail of a watch that such a sweeping view goes against the whole ethos of our hobby.
I could easily make an argument for any of the three brands to be the best/my favourite.
For Rolex I would point to their vast popularity (whilst giving a nod to the fact that many feel it is cool to dislike something if it is popular) and the longevity of their designs. I would also consider the irony that people hate on the brand because of its advertising, which actually proves that they themselves ARE effected btly advertising (albeit in an inverse manner to the intention).
If you want to say you won't believe something is brilliant just because the advert says it is, you should also accept that something isn't rubbish just because you dont like the advert (or size of the advertising budget).
Omega are easy to make a case for with such a wide range of iconic designs and technical achievements. Again, many of their designs have stood the test of time, and with just minor tweaks they are still supplying watches that closely match decades old designs without them being deemed retro or throwback because they have simply never gone away.
Finally, the argument for Tudor is a straightforward one, quality watches that compete in terms of quality with the big two above them, but at a significantly lower price point.
It is equally easy to take shots at each brand, but ultimately for me it comes down to my feelings about the actual watches rather than the brands.
Would I want a Submariner, BB58 or Seamaster 300 as my diver of choice?
Would I prefer an Oyster Perpetual, Aqua Terra or Ranger as my smart GADA?
And so on, I could make a coherent debate on my preferences on a specific watch from each stable against its closest comparison from the others, but ultimately it comes down to personal taste and personal opinions.
Because ultimately for me, all three of them make some lovely watches to a high standard, and all three have then leveraged these by mass advertising budgets (be that Rolex with the golf, Omega with the moon or Tudor with Beckham) to take their wares beyond our little corner of the market as collectors/enthusiasts, and on to global awareness.