First I will say I never played Vanilla before, I started wow with Wotlk.
The first thing you notice in Legion is how fast you walk. Walking speed is almost lvl 40 mount speed in Vanilla. Also of course combat in Legion is much faster and way more fluid, I felt like I was playing Diablo compared to Wow.
The the graphics of course are much better in Legion. So much more detail. They really did a nice job with the look of the expansion.
Questing: Questing in Vanilla is much more dangerous. If you pull too many, which is easy to do, you die. You always need to wTch where you are going. In both games I play Warrior tank. By lvl 10 I died about 15 times. Also I love the group quests. MMOs have gone away from this which is too bad. There are always groups running these quests so it is easy to get a group.
In Legion it is impossible for me to die questing. I can kill a rare elite and have 75% health. As a tank killing is slow but there is no danger, so I gather up a bunch of mobs and take them down.
The quest writing is vastly better in legion and a few quests have nice cut scenes which I like. The mobs scale to you, which for an expansion I don't mind. I hate it for a whole game like ESO.
Dungeons: in Vanilla dungeons can take 2 to 3 hours if everyone is at or below lvl. I really enjoyed these dungeon runs. They were a challenge and everyone needed to be on their toes. Classes mattered because every class a certain skills that other classes didn't. Loot mattered more because leveling was slow. At lvl 20 a piece would last you 5 hours of game play.
In Legion I have only done leveling dungeons, not the mythic. The dungeons are mind numbingly easy. As a tank I get aggro very easy and I seem to never have to manage rage. I always seem to have plenty. Rage is always an issue on Vanilla. The bosses have a lot more mechanics but they don't do much damage so you can just ignore most of them. I am sure this changes in mythic. The dungeons are super quick 15-35 minutes.
So in recap, I like both versions. They are completely different games. I prefer Vanilla because I like more of a social game. I am always grouping up in Vanilla where in Legion I join LFG and basically just play with NPC's as no one talks and there is no need of strategy. I will continue playing Legion as I enjoy it but look at it more of a single player RPG with decent story.