Super canon
Only going with the manga events, since the anime lacks a shred of internal consistency.
Vegetto probably ends up choosing to stay with Bulma as in DBM. Lacking enough people for the SSG ritual, Vegetto wishes for Tarble to be brought to Earth for the ritual, though is still beaten by Beerus. Freeza is easily dealt with and Vegetto solos the U6 tournament. With his strength, he then challenges Beerus to a rematch, though Beerus' skill and better stamina make up for his slight lack of power and Vegetto loses. He does become a regular sparring partner for Beerus though, the two gaining more power from fighting with each other. For the FT Arc, Zamasu would likely take Vegetto's body but considering Goku Black was still able to gain Zenkais whilst Goku wouldn't, I'd say this Vegetto would be able to do the same from his training with Beerus at a far faster rate to Vegetto Black. Vegetto Black still fuses with Zamasu, though would not have achieved SSR due to Vegetto not giving the two enough time and the fight would still be in Vegetto's favour. However, the stamina of SSB would bring Vegetto to a disadvantage eventually and he is forced to use the Zen-Oh button.
For the ToP, Freeza is still chosen for the team and Yamcha is put in as filler. With Vegetto's power, however, he easily solos the tournament regardless and Freeza isn't revived due to his role being far less crucial. Broly Arc never happens and Vegetto's power is enough that even without going all the way to SSB (or PSSB if he's trained to achieve it), would be enough to kill Moro before his energy is drained.
GT canon
Vegetto still trains Oob, though does so at Capsule Corp. By the start of GT, Oob is far stronger than in canon and Vegetto has made considerable gains too. Pilaf's wish goes undisturbed, though the Dragon Team eventually overthrows their reign and Vegetto, Trunks and Pan go into space looking for the Ultimate Dragon Balls once Dende informs everyone. The search through space goes far quicker with Vegetto's no-nonsense approach, though Baby still escapes to Earth. With little alternative and being unable to take Vegetto's body, Baby is forced to take full control over Gohan's body. Even if going into his 2nd transformation, this far weaker version of Baby would be unable to fight against even SS2 Vegetto and Bulma wouldn't have created the Bruits Wave emitter in time, with Baby being forced to retreat and being killed by a Final Kamehameha into the sun. Kibitoshin succeeds in erasing Baby's control from everyone (if still active) and the Ultimate Dragon Balls aren't used, allowing for Earth's Destruction to be avoided.
For the Super #17 Arc, Vegetto becomes trapped in hell, though is able to escape by doing a Vice Shout as Gotenks and Boo did. He arrives to fight Super #17 and does well in beating him up when using SS3, though things quickly turn around when #17 absorbs his Ki. The arc ends much as it did in canon once #18 shows up.
The Evil Dragons Arc is where things take a turn for the worst, however. Without achieving SS4, Vegetto would be at a disadvantage against the Evil Dragons. Even assuming he'd gained enough power his SS3 form was now as strong as Full Power SS4 Goku, he'd be outmatched against Yi Xing Long and, after the other Saiyans arrive to help, Super Yi Xing Long. With the tail restoration being too difficult to accomplish immediately, Elder Kaioshin would see no choice but to gamble using the Namekian Dragon Balls. Their lack of usage allows them to work, with him wishing for Vegetto to regain his tail and for a planet with the necessary Bruits Waves to appear near Earth. Vegetto gains what he requires to become a SS4 and destroy YXL. The ending is the same, other than Vegetto not leaving with Shenron and the dragon instead leaving alone.