There was competition, you just never knew about it. Asheron's Call was similar and out at the same time. Back then as far as 3d mmorpgs were concerned it was either Everquest or Asheron's Call, but no one knew of AC...
If there had been only Everquest, I would have played UO. I've never been a fan of Everquest.
As a side note, I still mourn
Ultima Online: Origin, the 3d ultima game. I had a Meer fire mage planed and I was really hyped about that game.
They cancelled it half way into production because they thought it would create competition for Ultima Online. You know, the old, isometric Ultima Online...