To be honest, I think some people are exaggerating when it comes to Minus-Bardock, or getting the wrong impression of him.
The original TV Bardock was, as pointed out, portrayed as just another soldier. He was a low-class Saiyan, in a team with four other low-class Saiyans, and aside from gaining some fame for he and his team's successful exploits, his name really didn't go down in history or end up remembered.
However, the special did still portray Bardock himself as "special" in some ways. He had a power level of nearly 10,000, which was way stronger than any other low-class Saiyan should normally have and trumped even —for reference— Nappa the elite's power of 4,000 or so. Then he got the psychic powers. Then he was the only one of his crew to survive against Dodoria. Whether it was luck or skill, Bardock from the TV special really was "special" in at least a few ways.
Then Naho Ooishi made him even more "special" in
Episode of Bardock, but I don't need to explain that to anyone.
However, the way I see it, Toriyama undid that in Minus. He scaled things back down in light of Episode of Bardock, and gave us an even "less special" Bardock than in the TV special. Minus-Bardock doesn't have psychic powers, he doesn't have people praising him for his extraordinary class-defying power
(he likewise isn't shown charging through an army of Freeza's elites, or anything like that). He's just an average low-class Saiyan who simply notices Freeza's odd behavior and acts on a gut feeling.
Furthermore, in terms of changes to Bardock's personality in Minus, I think that's kind of being blown out of proportion too. By no means is Minus-Bardock suddenly a "nice guy."
In the very first page of Minus, we see him smiling gleefully as he and his unnamed partner slaughter random aliens. He's still a murderous dirtbag who thrives on violence like pretty much every other Saiyan at the time.
The ONLY difference we see is that this "revised" Bardock has a soft spot for his wife and son(s). Even then, he's all tsundere about it, and blames it on Gine rubbing off on him. Heck, come to think of it, even Gine herself isn't necessarily painted as a "good person" in any way. She likewise only shows familial affection and concern for Bardock, Raditz, and li'l Kakarrot. But she's certainly not protesting Bardock's career choice, or anything.