My take on a rival: (Long Post)
I would like a stoic rival. A rival who is an anti-villain, who appears to be a jerk and appears to do terrible or cruel things to get what he/she wants, but in reality he/she's been trying to stop you from causing the utter obliteration of the world.
I would love a Pokemon game like that. The player starts out doing good, but unknowingly is the reason for catastrophic events happening. The clashes with your rival initially focuses on how his/her "evil acts" seem to be causing the world's spiral into armagheddon, but the more the two of you interact, the closer you get to your revelation. During one of your encounters with your rival (I'm thinking 4-6 battles total from your first meeting to Victory Road), you will can lose to him/her on one or two occasions (if once, you lose the first battle), if twice (you lose first battle and Victory Road battle, which means the rival will have strong and good pokemon with very good AI, and a few levels higher than the player during the encounters I mentioned). The rival's development comes from either wanting you either to die as well as being unable to accept an alternative to the situation to actively seeking out a way to fix this situation without requiring you to die. Which brings up the Elite Four as another source to correct the player's mistakes. However in this, the E4 are antagonists themselves.
By this point (or in Victory Road) your rival has gotten slightly softer (in that they are willing to work with you after your confrontation in Victory Road to convince them of a possible alternative to death), however your rival is still somewhat hesitant to work with you. The two of you clear the remains of Victory Road and like Gen V's BW, there's something in the way of E4 (could be the villain team's evil scheme, who tie into the E4 eventually). After the player, the rival (and possibly the professor who I'd like to be able to battle too), then comes the E4. The rival goes through the E4 first, but loses to the Champion just moment before the player shows up.
The player defeats the Champion, and is able to find an alternative. So then the player, professor, rival, and champion travels to a secluded far off island (gets mentioned earlier in the game) that holds all the answers and the true reason to why the player has been causing all of these horrific events, leading them all to meet a character (or pokemon) that exceeds the power of the champion. If it's a character, they have servants for the other three to fight. If not, then the Pokemon prevents the other three from being able to hurt it and only the player can enter battle against it. After defeating it, somehow the problem is solved, but the game foreshadows a new problem that will arise in two year's time.
I don't think this would be that good, but I'd love another pokemon game where the gym leaders or even the E4 plays a pretty large role in the main story. I'd have your rival, professor, some gym leaders, the evil team, and the E4 (and the character stronger than the champion or Legendary Pokemon on the secluded island) all take part in the plot. This way, the rival would probably play an even larger part in the story by actively going hand in hand opposing you, while cleaning up some of your unintentional messes. Your rival would be a in his/her early twenties. If the rival is a female her name is Bliss. If the rival is a male, his name is Jericho. By the end your rival is a friend of yours, but doesn't associate with you. You'll be able to find him/her on another island at the top of a tower. Rival says stuff about the adventure and all, gives his/her respect to the player, challenges you to one last battle to ensure that you'll be ready to defend the world once again when time arrives. Afterwards, rival disappears leaving a note behind at your house, detailing where he/she headed off to, and wishing you good luck.