I'll just long-post since I'm not doing anything.
Theme - Crimson
Have to go with Crimson here simply because I prefer the theme and atmosphere of the biome. I know fleshy, visceral gorelands have been done plenty of times in videogames before, but so has the more nonspecific "infected" evil that the Corruption conveys. The red of the Crimson also strikes out at me more than the purple of the Corruption does, which serves a more mechanical purpose for easy identification in Crimson Ice biomes where the red ice really stands out compared to the purple ice of the Corruption (thus making it easier to clean). In addition, I prefer the Crimson BGs, even though the Corruption BGs recently got an update in 1.4 that provided them more variety than just the purple trees and dead tree BGs that they were restricted to prior. This Crimson BG with an arch and skull in the background with the sprawling red hills is my favourite evil biome BG. The red and black of Crimson Deserts is also appropriately edgy, severe.
World Generation - Tied:
Was originally going to give this to Crimson again because the Crimson chasms destroy the landscape less when generated, which is admittedly appreciated, but the Corruption has advantages too. I think a purified Corruption chasm looks quite neat, leaves an unusual amount of stone blocks on the surface and acts as a sort of natural ravine you don't usually see in pure biomes. The Crimson generation is also more annoying to purify because there's a good amount of Crimson that spreads well past both sides of the chasm horizontally, while the Corruption that's initially generated tends to hug pretty close to the chasm, making it easy to purify, especially since you can just drop in and out vertically. I will say that the Crimson chasms sort of look like either a grasping hand, or a heart and veins, which is cool.
Music - Corruption:
Both of them have fine tracks, the Corruption seems more classically "spooky" and investigative while the Crimson soundtrack is more grating and unnerving, thus it does make the Crimson nominally less inviting to be in. However, the Crimson soundtrack is too discordant to be appealing to listen to, even if it's supposed to be discordant to fit the aesthetic. The surface and underground Corruption themes are more consistent and harmonic, I prefer listening to them.
Enemies - Crimson:
Probably the only category I can easily give to the Crimson. The Corruption has some variety but all-in-all seems to just take the Eater of Souls and modify it a bit for most enemy types. Devourer is an elongated Eater of Souls, Eater of Worlds is a larger Devourer, Corruptor is a larger Eater of Souls, World Feeder is a bloodshot Devourer with more eyes, even the Clinger is a play on the Eater of Souls. Essentially, most of the enemy types are based on the formula of "brown cyclops creature with protruding teeth". The Crimson in comparison doesn't re-use many enemy types, each Crimson enemy is different aesthetically and even mechanically in most cases from the rest. They do use some of the same AI as other creatures (Face Monster just uses Fighter AI), but most enemy types share AI with another enemy. The Crimson has more aquatic variety to boot, which helps with immersion. Both have their contrasting goldfish variants but the Crimson additionally has the Blood Jelly and Blood Feeder, the Corruption has no counterpart to these. Corruption has too many worms as well, and I hate Worm AI with a passion.
Items - Tied:
I'd have to generally go with the notion that the Corruption has better pre-Hardmode items, while the Crimson has better Hardmode items. Contentious category but I never seen the crimson hearts to drop items with as much utility as the shadow orbs. Musket is generally thought to be better than the Undertaker and the Band of Starpower has more utility for mages than the Panic Necklace has for other classes. The light pets are more or less equal, though I prefer the Crimson Heart seeing as it appears to be somewhat faster and more dynamic, bouncing around and spouting blood everywhere. Since the Brain of Confusion was buffed it's been on better terms against the Worm Scarf though I still have a slight preference for the latter simply to further boost my defense. On another note, the Fleshcatcher (22% fishing Power, 13.5 velocity) is objectively better than the Fisher of Souls (20% fishing Power, 13 velocity) which is interesting considering how on all other notes the Crimson and Corruption are designed to be equal alternatives with trade-offs in one department for an advantage in another department. With the fishing poles the Crimson one seems statistically superior with no real sacrifice. The Corruption also has leather, I guess.
In Hardmode, the Crimson makes up for it a bit. Even with the Ichor nerf it's still a great debuff and readily attainable, so I think it still carries more worth than the Cursed Flames do, DoT was never that substantial in Terraria considering how much health every enemy has. Bladetongue is more or less on par with the Toxikarp for their respective classes, but the Flesh Knuckles offer more crafting benefits to the Berserker Glove than the Putrid Scent does to the likes of the Recon Scope or Stalker's Quiver (which only inherit the aggro-reduction, none of the damage or crit bonuses). Vampire Knives were also a very powerful weapon on their own at the Plantera stage (and my main weapon for melee even against the Empress before fighting Golem). Scourge of the Corruptor is also a powerful weapon at the Plantera stage but I didn't find it to carry long beyond that since it lacked the niche healing utility the Vampire Knives had.
So, totaled I'd prefer the Crimson, but not by any significant margin.