He believed that Goku was on the planet for one day only, and that he'd never get the chance to fight him again.
He didn't even think about winning/fighting against him until he realized he could get a free powerup because after the Yakon fight he knew he'd get his shit pushed in.
He had to swallow his pride and accept help from an evil space wizard, which is basically admitting defeat in Vegeta's mind.
Now that Goku is there everyday, you don't see him challenging him with that same intensity because he knows he isn't going to fucking disappear forever the next day, and he knows he would still get his shit rocked. MUI exists now and Vegeta has seen it firsthand.