I think Discord has superior hax and more versatile control over his abilities compared to Bowser. Though at the same time, Bowser has a harder shell (No pun intended), he'll likely take things a lot more seriously once the fight begins. He as well has the AP advantage I believe.
Now, Bowser's hax aren't unimpressive, he's shown a decent array of them a certain amount of times in the past. He can alter Discord's emotions with the Vibe scepter, BFR with his stomach, or even nullify his power. On the other hand, Discord has mind hax, transmutation, and likely better reality warping.
In a scenario like this, similar to what GyroNutz said, I feel it's in the matter of who hits first. Knowing he'll take this more seriously, I feel Bowser would want to give off the first hit, as Discord is quite arrogant and cocky, but despite that I also feel Discord would as well be wary of dodging the first hit via teleportation or regenerative decapitation.
For now, I'll vote inconclusive. It's in a matter of who'll hit first but at the same time, at the current moment at least, it's just a bit too difficult to gauge of who'll make the first hit onto their opponent.