I enjoyed the TNT decklists a few years back (pre-Innistrad), since I liked the threat density that comes with Burning Wish, but I disliked the compromised manabase and color requirements of TES (which I have never been able to do well with).

I've decided to take a break from playing fair after doing so for some larger tournaments, and I took ANT to two weeklies (a list very similar to Adam Prosak's). I was dismissive of the list initially, because I could not imagine playing only 4 tutor effects, but I managed to go 8-0 against Miracles, Goblins, Elves x2, Bant, UR Delver, Jund, and RUG Delver.

A couple observations from my perspective as a storm player who has returned for a 3-year hiatus to play these newer variants:
1) The addition of Gitaxian Probe makes it allows for a lot of "easy mode" games where you would previously have to guess about what you were willing to play into. The fact that it gets us closer to threshold, digs further for no mana off Past in Flames, and more cheaply enables tricks involving Brainstorm + LED (with Tutor/business on top) is just gravy.
2) Past in Flames is absolutely ridiculous in this deck. I occasionally miss not being able to rebuy Lion's Eye Diamond with IGG, but Past in Flames is so much safer against blue decks. The flashback is surprisingly relevant if you're able to generate a ton of mana and your first attempt gets countered, but also if you need to bin Lion's Eye Diamond to enable the card. There are also a ton of games where I need to play Past in Flames in desperation mode without access to a tutor, and I'm able to eventually find the win by sequencing cantrips.
3) 12 cantrips + 4 probes + 4 Infernal Tutor still does not provide the "business density" that you get with TES/TNT; however, there are a lot of games with the latter decks where you have two or three tutor effects, but no easy way to get ritual effects, and in these cases, the extra cantrips of ANT shines.
4) Taxing effects are incredibly easy to play around for ANT compared to TES. Cabal Ritual is far superior to Rite in Flames, the reliance on only a single red mana at most to go off, and a relatively resilient manabase all contribute to this.
5) I thought this deck straight up loses to Surgical Extraction. I underestimated how easy it was to peek at their hand and cantrip into a discard effect.
6) Playing with a full sideboard is amazing. I actually think G/W or mono-white decks with hatebears and a mana denial component represent a more difficult challenge than a wall of countermagic. Being able to board in several cards to actually answer these permanents is terrific.