Pre-Hardmode, especially back in 2011. The feel of not knowing anything about the game and it's potential was nice. Learning all of the mechanics from scratch is wonderful when you're doing it on such a fantastic game. Boy was I in for one hell of an adventure!
I would say my favourite would be pre-Hardmode ~ everything kinda fits together well pre-Hardmode, and the items you get seem to have a sense of normality. Flick the Hardmode switch, and that sense of normality gets thrown out of the window and is replaced with five times as much wacky - and while I do enjoy the wacky and insane Hardmode stuff.. there's something to be said about wandering a pre-Hardmode world with endgame pre-Hardmode gear.
Hardmode Terraria kinda feels like an MMO, with adventurers looking more like they were just showing off with sillies rather than actually gearing up for a significant threat. It's hard to take a guy seriously when he's wearing a turtle and throwing donuts of light around everywhere. (Though I say all this, Cobalt Armour (with Hat) is my favourite armour set in the game, next to Meteorite)
I don't like either more, I liked them both for separate reasons, pre-hardmode is fun for exploring and learning the game, Hardmode is fun for re-exploring(if that's a word) and completing objectives, I like both parts