This was an interesting take on Dragonball Z movie #1 by MistareFusion, and it's actually a movie I know very well.
None of the movies in DBZ era are canon, however fans have tried to fit them somewhere into the TV series timeline, the problem is as been discussed, as this creates some contradictions with the story, at the point of movie #1, if we are to treat it as a pre Raditz battle story, Piccolo and Krillin weren't even supposed to know Goku had a son, let alone be made aware of his special powers, so there's no way to reconcile how Garlic Jr would fit into the main plot.
I do wish some of these movies were canon, but they are not and logically they couldn't be for obvious reasons, plot contradictions and not based on manga material. Then again the TV series wasn't without its problems either, and Vegeta's redemption arc sucked in simple terms. The way they handled his redemption didn't make a lot of sense, as he had complete control over whether or not Babidi had invaded his mind and given him a power boost, as well as the atrocities he committed at the martial arts tournament.
Even later on "as a changed man" he was still sort of a jerk, and just because he is no longer a "mass murdering psychopath that kills innocent people" it doesn't mean he still doesn't have issues to work on, into Dragonball Super he was still overly obsessive with his rivalry with Goku to the point of insulting him and berating him over the smallest of things, like not wanting to be outdone in training, because he is this "royal saiyajin who just shouldn't be surpassed" which only displays his own narcissism, he thinks of other's as lesser just because he is of a royal bloodline, I admit Goku doesn't make the best decisions, but then neither does Vegeta, historically in the franchise, even as a so called ally of the Dragon Team post Frieza arc, he nearly doomed planet Earth, twice, the second, if Majin Buu were allowed to win, this would've resulted in the death of both Supreme Kai and Beerus, I know this is hindsight as a result of the Super series introduction, but this does matter, what if Zeno took issue with Buu running amok as a result of the bad choices of Earth's "heroes"? universal genocide time.
And all this is after Vegeta just got done admitting to Goku close to the end of the events of Dragonball Z that Goku was better than him when Goku was fighting Majin Buu and when Vegeta was reminiscing over the good deeds Goku does and the risks he takes for other's as a result of his pure heart.
And on the subject of Vegeta redeeming himself, I do agree with MistareFusion in saying, I do think the fictional character Vegeta being mind controlled and not being in control of his actions as a result, would've made his redemption arc much more acceptable to swallow, instead of Vegeta making the conscious choice to be taken in by Babidi just so he could have an epic show down with his rival Kakarot and nearly dooming the inhabitants of Earth, perhaps the entire universe with it, in the process. If you're going to humanize a character and try to make a story about redeeming a bad person, through change of personality, this isn't the best way to show that. Vegeta remained a serial killer throughout most of Dragonball Z, and only after realizing just how bad he messed up after his initial fight with Buu, did he sacrifice himself with the hope his family would live on.
Vegeta should've began the redemption process in my opinion during the events of the Cell arc, having an epiphany inside his head after seeing Cell get his final form and realizing that evil actions are their own undoing, then ceased being a serial killer after the fact, even though back then he was still evil as he wanted to defeat Goku and destroy him for petty reasons, and would have done if Cell's actions weren't the obstacle in achieving that goal. As stubborn as Vegeta is meant to be portrayed, I feel his redemption would've been more earned if this were to be the case, and if his eventual show down with Goku in the Buu arc wasn't done by choice. It would be easier to sympathize with a changed man who was forced into violence and doing unspeakable acts against their will, than it would be if they were to do these things because they were selfish.
I haven't seen all of Dragonball Super, but I know enough about it to know it left less of an impression compared to previous series of the show, naturally this would extend to the manga as well since this is what the TV series without fillers would be based upon.
Was Super worse than GT? I can't say for sure, as I have not seen enough episodes to make that conclusion, I will say this though.