Strength wise, Beerus has him beat possibly. But if Omega Shenron is def serious from the start, he could just use the negative energy & destroy the universe. Something Beerus was afraid Zeno might have done. lol
While Omega is waiting for his negative energy to slowly nibble away the universe, Beerus uses a fully powered Beerus Ball to instantly destroy the dragon, as well as whatever universe they're fighting in.
Not really. Omega Shenron is legit. He can def. beat Beerus overall as the negative energy destroys the Universe along with Beerus in it. Plus, you need to purify Omega Shenron's Negative Energy or else he will keep coming back. lol
SSJG Goku > GT based on feats and statements. So Beerus, who is ridiculously stronger than Godku, could erase Omega out of existence with absolute ease.