I don't particularly dislike them, but.. for me an Omega replacement should be
cheap(er than equivalent opposition)
maintainable from a large dealer network
badgeless (so not one of the 'big boys' Audi, BMW, Merc, Jag)
Surprisingly spacious and practical
Infiniti/Nissan comes under this, Lexus used to, though they've really become a premier brand and shaken off their Toyota roots in most eyes now. Skoda or Seat, too, I'd see as a contender, to a lesser degree a VW. (I do like Phaetons) There's not much out there these days. Rewind to the good old 90s and you had to choose from...
Rover 800/600/75
Frod Scorpio/Granada
Toyota Camry
Peugeot 605
Citroen XM, or go a bit older - CX
Vauxhall Carlton/Senny/Omega
Renault 25 / Safrane
Fiat Croma/Lancia Thema/Saab 9000
Now there's really no non-swanky brands making executive cars any more. The Omega was about the last, apt, considering where it sits in the Greek Alphabet.