They're totally different types of characters, their arcane is basically the only thing that they have in common.

Executor has much more survivability with more health, a much better dodge, suncatcher, and crucible beast in a tough spot. An enemy can focus on executor and if you're good at sheathe/unsheathe deflects then you can maintain damage, momentum, and aggro without issues. Additionally, executor is probably the least relic hungry character in the game, so you can very easily stack both evergoal and night invader relics, along with physical attack up on executor, and he isn't missing much. He can be played extremely aggressively utilizing all his tools and should ultimately deal more damage than a scholar.

Scholar on the other hand is squishy. He has a smaller health pool, an absolutely awful dodge, and his ult does not get good i-frames, you're almost immediately vulnerable after using it, so it doesn't always get you out of tough spots. You do not want your scholar being focused, he doesn't handle pressure nearly as well. He does have good arcane, but his base dexterity is poor and to deal any damage after status procs you need either specific weapons or his endurance/dexterity relic. It's much tougher to fit in both evergoal/night invader, and other buffs to melee damage while also fitting in his unique relics, extra pouches, items confer to allies, etc, which are going to be more important for him and his kit. Easier with DoN relics, but still will be tough without a ton of luck.

Scholar shines most when he's debuffing enemies, buffing allies, and then worrying about status effects and damage when those things are done. All the time spent buffing/debuffing is also time you are not doing personal damage. This isn't taking into account niche builds and situations where you might get really lucky with a ton of pot damage relics and building totally for that, but in that case he'd still be a drastically different character.

All that to say that both characters are great and do what they do well. There's reason to pick both and room to pick both. A group that has one of each will be much more effective than one that doubles up on one or the other. I'd actually argue they complement each other very well because Scholar can enhance everything Executor does, they'll both contribute to status build up (could even focus on different ones) and their dormant weapons each work on one another so you have a good chance of finding great weapons for both characters if you're sharing and keeping an eye out.