Normal Crota is simple if you have a team that knows what they're doing and you can be carried. Vault requires almost everyone to know what he/she is doing.

Furthermore, and most importantly, normal mode allows revives, which allows a lot of sloppy play.

EDIT:

Things you need in vault: oracle killer, scout rifle, sniper rifle plus telemetries ideally icebreaker, lots of void, coordination.

Things you need in Crota: rocket launcher.

EDIT 2: Assuming at least half of the team is 31+. If not, then Vault.

Imagine, if you can, that you're a mere mortal, without the ideal armor and every freaking raid weapon or exotic.

Imagine, if you can, that you're a deeply flawed raider.

Depends on my level. If I'm 30, VoG Hard is easier (and Crota NM is a nightmare). If I'm 31-32, Crota Normal is probably quicker, and revives make it a much more casual experience. An experienced sword-wielder can make or break the final fight, though.

No revives, and everyone has to know all the different jobs at Atheon. I'm a reluctant relic holder for Atheon (though I'm awesome at it at the Templar. I don't get it either), but I know what needs to be done if I need to do it. You need at least 3 other people to know all the jobs to complete it (that way the worst combo of three still has 1 relic holder in it). Crota, you need one person who knows how to handle to sword and everyone else just shoots things.

Assuming you're going in at raid-par level (VoG hard at 30, Crota normal at 30) I'd say VoG Hard mode is way more difficult. The Templar fight requires rock-solid play from the relic holder, and heavy damage from the rest of the team. The Atheon battle can take a lot of time to figure out because there are so many different roles to fill (plate-holder, relic carrier, oracle killer, etc) and everyone on in the group needs to be ready to fill every single position at a moment's notice. If just 1 of the people who get teleported don't know what to do, it can be a disaster.

Crota, meanwhile, allows more clear-cut defined roles for everyone to play. Everyone has their moment to step into the spotlight with the bridge section, but if 1 person drops the ball it is still possible for the rest of the team to recover and carry on. The most difficult part overall is the deathsinger, but again it only takes a couple people who really know what they're doing to carry the rest of the group through.

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VoG hard mostly due to endless Atheon glitches and no revives.