I think mbaccari99 makes a good point about the strict evaluation. If the job is to make someone's spell stop happening,
Counterspell just has fewer things to worry about. That's why
Counterspell is the card of choice if you need to protect your own state, like CleanBelwas said. It's in the gray area of wanting to stymie your opponents but also wanting to be more active where
Arcane Denial becomes appealing.
The impression I'm getting is that people who prefer
Arcane Denial (or the places they prefer it) are all about situational advantages. If you've built a deck to be able to easily deal with threats, or if you are considering a political multiplayer environment, or if you've got something mean planned with
Hullbreacher (or
Notion Thief, or
Fate Unraveler, or
Nekusar, the Mindrazer, or
Xyris, the Writhing Storm, etc.), then
Arcane Denial's drawback can range from "no big deal" to "actually an upside". And like The Golgari Guy said, in a
Talrand, Sky Summoner or
Noyan Dar, Roil Shaper deck that just wants cast triggers and card draw, countering your own do-nothing cantrip to refuel can be a pretty decent play.
I guess what I'm seeing is that the praise for
Arcane Denial isn't because it's a better counter then
Counterspell, but because it's a toolbox that activates on countering a spell. If I'm already on the ropes,
Arcane Denial is probably just going to put off losing, which might be enough but isn't ideal. But if I'm in a more dominant position,
Arcane Denial can be used to advance my own state if I'm smart. Maybe even comparing it to
Counterspell isn't as apt as it seems, and it may be more like
Overwhelming Intellect, which should probably not be evaluated as a counter but as a draw spell with a counter condition. If we compare it to something like
Vision Skeins (which is terrible on it's face but exactly what you want in the proper context), it's easy to image that the best home for
Arcane Denial is in those decks that punish players for cards in hands or for drawing, or that have some other asymmetrical effect to exploit. That doesn't mean it's bad everywhere else, but I would say that it shows that
Arcane Denial is probably
different from
Counterspell rather than a better or worse version. Luckily, we're allowed to play both