This is going to sound like a total cop-out answer, and it technically is, but I'd say that I don't really have a favorite rival. While I like some rivals more than others, I don't really feel strongly enough about any single one to rank as my favorite (or least favorite, for that matter).
I really like all three Gen 5 rivals, but I think Hugh is my favorite. He can be really mean and edgy but has a softer side for his sister and is pretty passionate about being a Trainer. It's a nice and complex combination of traits that I wish other rivals had. Gladion comes close though.
The Gen 5 rivals take first place for me. To me, they were friendly rivals done right (jerk rivals are overrated). While, to me, Hugh was a (small) step down from Cheren and Bianca (though his team was better than Cheren's, who was the more competitive of the two), he still had many strengths that made him memorable and overall a good rival. But, if I had to choose just one of them, I'd go with Bianca, as she got probably the most development out of the three, and her post-game team is actually quite robust and balanced with good synergy, which was surprising considering she's more of a hobbyist than a serious trainer, though I did welcome it.
Second place goes to Barry due to his fun yet competitive personality. At least when you meet his father you can see where he gets it from. He also goes through good character development during the story, so that's an added perk. He also had a very good and well-rounded team that really took advantage of things like TMs and such. His AI wasn't too shabby, either, thereby allowing him to use pretty solid tactics. He also dethroned Red for a bit due to his team becoming the strongest of every character until HGSS rolled around, so that's an accomplishment worthy of praise.
Third goes to Hop, who is basically a Galarain Barry (something that I took note of pretty quickly when I first started playing). He goes through probably the most development of all the rivals, especially since most of it was on-screen (unlike Bede's and Blue's off-screen and shoehorned development, the latter of which took until Alola for him to actually be decent, which was too little too late). The fact he also ultimately found his future and even caught the opposite Legendary is something that's never really happened before. While his "future champion" bragging got very annoying pre-character development, especially in repeated playthroughs, he ultimately succeeded in becoming a rival worth praise.
My personal favorite is Silver. The mystery surrounding him and his dad Giovanni was amazing especially since we had to speculate about it for years with vague hints from the Fame Checker and the Pokémon Special manga. When it was finally confirmed in HGSS through the super secret time travel event I was so excited I could feel it in my toes.
I love Bede as well but the fact that he never interacts with Rose again after "the incident" kind of leaves you hanging. I am also confused about their relationship because Rose doesn't even recognize him during their first scene together. Bede loses some points because of that but I adore his relationship with Opal. Although it's kind of sad that she will probably die soon which means he will be all alone again...
I think Hop is my new favorite rival. I just thought he was really endearing and likable right away. Even talking about how he wanted to defeat Leon or start the next chapter of his legend didn't bother me because the excitement just seemed so sincere. That and I just felt bad because I knew that he wouldn't be the one to defeat Leon. I loved his character development. Unlike a lot of other rivals, the constant defeats clearly did affect him, especially after he lost to Bede, and changing his team around, to the point where he took out his first Pokemon, really showed just how hard those losses hit him. Hop lost what confidence he had in himself and it took him a long time to really regain it. He managed to find a team to stick with, so he was at least less indecisive at that point, but losing still affected him a lot. In the end, he found his own strength with his love and kindness towards Pokemon, which allowed him to earn the trust of a Legendary Pokemon and then ultimately find his own goal. He's just easily one of the most well written rivals in the series. I've been loving the Isle of Armor DLC, but one reason why I'm looking forward to the Crown Tundra is so that Hop and I can both defeat Leon in battle.
Bianca would be second. She felt really refreshing to me at the time because similar to Hop, losing did have an impact on her. She was always weaker than Cheren and she didn't feel like she was capable of getting stronger. Even though Hop's losses affected him, he was still one of the strongest Gym Challengers and got to the semi-finals too. Battling in general was a challenge for Bianca, but I don't think she was particularly set on becoming a strong battler like Cheren was. I really liked all of the fifth generation rivals, but I always have a soft spot for Bianca and I really loved seeing how happy she was as an assistant during B2/W2.
Silver would be third. I still feel like the concept of the jerk rival is overhyped, but I think Silver was one of the few jerk rivals that was done well. He wasn't just a jerk for the shake of it like Blue was, but he was a bit more like a villain given that he stole his starter Pokemon and was so against the notion of bonding with Pokemon. His development was pretty solid and satisfying. I do like how his change towards his Pokemon is a bit more subtle in a sense with his Golbat evolving into Crobat too. I liked that he was willing to return the Pokemon he stole in HG/SS, but also happy when he was told he could keep it. It would have been nice to see that scene, but it was still pretty touching to see that Silver had been able to bond with his Pokemon after all.
As a side note, I am somewhat surprised that Bede seems to be relatively popular. I can see why when he starts off as the jerk rival and changes near the end of the game, but I thought he was way too stuck up for my tastes during a good portion of the games. I like where Bede's story goes, how his eyes look clearer/happier once he becomes a Gym Leader and how he ultimately decides on restarting his path with a new goal in mind, but he just was too annoying for me whenever I talked to him. I do like Bede, but it just took awhile for that to happen after I reflected more on Sword/Shield.
It might be an unpopular opinion but I really like Gen 5 rivals, Cheren and Bianca. I felt that them being all friends but still rivals who had just the right amount of competitiveness between them was great.
Cheren feels competent enough to be a serious rival, but never becomes a jerk like Blue or Silver.
Bianca has very nice development and even though she's friendly, she's not overly so. You also have to take her seriously. By the end her team is very well balanced and can give you trouble if you're not well prepared.