Stamina: Abraxos, Extremely High > Azurills regular High.
Range: Azurill, hits at max 10 meters with its tail compared to Abraxos several meters (2-9 meters).
Intelligence: Supposedly Abraxos, as Azurill is naive, but that doesnt mean Azurill cant fight.
Experience: Equal? Abraxos age is unknown and Azurills can vary.
Abilities: Azurill. Remember the time I said “At first” earlier? Well this is where it gets played. Tail Whip is pretty beneficial to lower Abraxos defense, down to 25% of Abraxos original attack from stacking it 6 times (the max). Azurill is also able to lower Abraxos Attack via Charming it. By the time the debuffs are applied, Azurill now takes the AP and durability. While I see that Abraxos can fly, special moves should be beneficial, especially Bubble Beam, which can lower its speed (but its a 10% chance of landing the slow effect). Abraxos can hide, but it cant delay its fate once the effects are applied. Assuming this is Huge Power Azurill, that makes it a HUGE advantage once the wyvern is weakened. And if its on the ground, Slam does high damage, and adding up to Abraxos debuffed from the Tail Whip, this WILL do extra damage and it will most likely be defeated within a few good hits.
Conclusion: Azurill pretty much takes this via Bubble Beam to slow the wyvern down first, then debuffs it to make it weaker. Abraxos as far as I can see does not have any projectiles, so it has to get close to attack but then it will be Charmed, Tail Whipped, Bubble Beamed, or even another good attack that will take down this wyvern.
Abraxos will immediately take the battle to CQC, using his teeth and claws to rip at Azurill (note, this does not mean he will land, he tends to remain in the air to allow himself range of motion and to bring his tail into the equation). I highly doubt cuteness will factor in here, Abraxos is a highly trained and vicious creature that has been pitted against other wyverns since the day he was born. If he's willing to kill the ball of water, he's gonna throw himself entirely into the battle.
Azurill has abilities that can change the flow of the battle and bring Abrazos to his knees after time. But Abraxos isn't gonna let him use em. The second the battle begins, Azurill is going to be fending off an endless wave of teeth and claws and tail. Azurill can get a couple of hits off, that means nothing. Abraxos can take a pounding while still dishing it out.
The main way I see Abraxos getting around that is the 10% chance of slowing. Abraxos is Transonic and only meters away from Azurill, it will be less than a second before the two combatants are on top of each other. And I don't know of a Pokemon that attacks with the sheer viciousness of Abraxos, Azurill isn't gonna have time to throw his moves when he is being ragdolled by a blur of teeth and claws.
Also Azurill attacks a lot faster than Abraxos does (Transonic >>>> Superhuman) with numerous moves and strategies to keep Abraxos at bay such as bubble beam, slamming the beast with its elasticity tail or singing to put him to sleep. Huge Power, which doubles the user’s AP, should give Azurill the ap advantage, and it being level 100 means it’s no slacker when it comes to fighting experience.