I've never even heard The Slip (since I'm not even remotely a NIN fan besides HTDA), so I wouldn't know
I don't agree. It sounds more like The Slip than With Teeth or Year Zero. Much more in common with NIN's earlier albums, though, as it's more raw (and less live instruments). Not all that similar sounding, though, but to say absolutely nothing is a bit of an overstatement.
I'd definitely have to disagree here. HTDA feels a lot more like Year Zero to me, with a mix of Ghosts for good measure.
There are some similar beats in HDTA to Year Zero and With Teeth, but I'm saying the production is a lot more The Slip and earlier NIN stuff. But there's quite a bit of Ghosts in there, yeah, that's a good comparison.
By the way as far as thinking the EP sounds like the Slip, I'm somebody who literally listened to it once and went "meh". It's not bad, just not something I'd go out of my way to listen to. I'm thinking it'll be a good idea to take a new listen though.
I think the full length album will sound more its own than NIN. As Trent said the EP was just a experiment and the outcome sounded good so they released it.