What if vegeta had destroyed cell when he actually had the chance to instead of letting him become complete ? Well we can obviously assume hot after his win over cell, vegeta would be desperate to fight goku ! Vegeta would have it tuned in to his head we was untouchable and no one could would be able to beat him which he would quickly discover that he was still majorly out classed and far behind goku by miles. (Assuming vegeta chalanged goku when both he and gohan came out the HBTC)
Seen as cell was defeated before he achieved perfect form ... That would mean trunks wouldn't have fought cell , the cell games would not have happend , gohan wouldn't have become Ssj 2 Atleast against cell anyway and goku wouldn't have died therefore meaning he wouldn't have received any of the training he learned in other works from he died in the series till he came back 7 years after.
this is where things get a bit "what if" If vegeta destroyed cell that would mean we wouldn't have a legit saga again till the buu saga but it was suggested the first broly movie took place in the wait for the cell games ... So in place of the cell games arc cloud a broly saga have been a good fill in ? Personally I feel it could have been because broly was suggested to be stronger than PERFECT cell in his first movie( which I agree with) so gohan could still have achieved Ssj 2 against broly. Afterall broly wanted only "kakarot" so gohans emotions still could have been triggered by seeing his dad about to be brutally killed. A canon broly arc would have been a great substitute for the cell games IMO if vegeta had actually destroyed cell. I actually think it would have been cool to see a broly arc in the original series aka cell still becoming perfect etc. But anyway back on topic .....
If vegeta had also defeated imperfect cell we would not have had a bojack movie. Cells explosion on King kais planet was the cause of bojacks escape.
Now we come to the 7 year gap
If vegeta had destroyed cell , like I mentioned already goku would have been alive therefore meaning vegeta would still have a goal to surpass. He became more of a family man within the 7 years of peace mainly because he didn't have goku around so we can assume vegetas attitude towards life would be still to surpass goku instead of like taking trunks to the park etc etc etc.
gokus pressince alone would effect the likes of gohan by still making sure he trained and stayed strong instead of completely turning to the books.(keep in mind it's still a what if scenario if gohan would be ssj2 or not) goten and trunks would most Likley be trained by goku ... Afterall goten and trunks hung out etc and I'm sure goku would have no problem playing a teachers role to trunks whenever he came and visited goten essentially meaning potentially goten becoming stronger than trunks by the time the tournament came around. Piccolo would maybe even join the fray to and teach goten while goku and gohan trained with each other at a higher level. Assuming goten was even born actually because he was said to have been born after the cell games. Aka goku n chichi got hot n sweaty during the cell games wait lol. Krillin and the rest of the Z fighters would also still continue training most Likley if goku was alive. Brolys second Comming may not have happend also if there was a broly arc and gohan became Ssj 2 and destroyed him but say he still survived and came to earth the plot for second Comming alone would be way , wayyyyyy different.
the buu saga !!!!!!!
by the time the buu saga comes around the supreme Kai would still warn everyone about buu. goku maybe wouldn't have achieved ssj3 due to training on earth instead of the advantaged otherworld unless he achieved it through training on King kais planet but we can assume he would 100 percent have achieved ssj2 and that goes for vegeta too. and gohan if he hadn't already achieved it against broly (what if theory). But by the time the fights happend on babidis ship I personally feel Dabura would have been defeated and the buu saga would have ended there unless vegeta still became majin but babidi wouldn't have Dabura to guard him meaning he would get killed too.
If I have missed out anything you would like to add please feel free but IMO this is roughly what would happen if vegeta killed imperfect cell with a few what ifs flung in :) thanks guys for reading have a great day !
onwards to the buu saga.