I know a lot of people who watched Breaking Bad who don't watching Better Call Saul, mainly because they just see it as a spin-off show that wasn't worth making. It is a shame too because while this show includes a lot of Breaking Bad references (obviously), this show stands on its own two feet. In some ways, it flat out surpasses Breaking Bad.
There are just a ton of characters to enjoy. For as good as Breaking Bad was, I don't think it can match Better Call Saul in character depth. Rarely did something happen that involve Walt and Jesse, which isn't a bad thing necessarily but meant you couldn't have a lot of scenes that revolved around other characters. Even with someone like Hank, a lot of the interest in him came from being Walt's brother-in-law and the suspense of when he would finally find out. There wasn't a lot of character development though. Better Call Saul nails character development for everyone. The least developed character would probably be Howard, but he doesn't need it - he's flawless in his role.
Seeing the growth of Jimmy, Mike, and Kim has been awesome. Kim in particular is an outstanding character and they get right with her everything they got wrong with Skylar. I liked Skylar more than most, but she was still treated as someone who just bounced off of Walt rather than stand on her own two feet. With Kim, she is her own woman. She is a complex character who strives to be moral but Jimmy is capable of swinging her back and forth, and the recent development with Jimmy/Chuck shows that.
Then you have Gus Fring, who was an obvious addition to the show considering the timeline. But he isn't the Fring he was in Breaking Bad. It has only been two episodes but he is so much better, which is incredible considering he was already good in BB. Watch Episode 4 of Season 3 and you will see what I mean. In that episode, we didn't see Saul, Kim, or Mike until damn near halfway through. Gus, Hector, and Eladio were absolutely brilliant. And the show is just so well directed.
There are so many other characters as well on the show that just play their role so well. I know there are some people on here that watch Better Call Saul, but definitely make sure to keep up with Season 3. It's been great.