60% of levels favor the arcanist—
—but the wizard is much stronger the other 40%
At all even levels, as well as 1st and 19th, the wizard and arcanist have access to the same spell level. That’s twelve levels, or 60% of them, while the wizard is ahead on the remaining eight levels, or 40% of them.
When they have access to the same spells, the arcanist is superior. The flexibility of deciding on-the-fly how many of each spell to cast is awesome. But keep in mind that the exploiter wizard can—and probably should—take the Quick Study exploit, to get a similar ability (albeit at the cost of a point from the arcane reservoir). So the real difference between the arcanist and wizard here is that the wizard’s flexibility is limited by the arcane reservoir, rather than the arcanist having it and the wizard simply not.
The other differences are the greater number of exploits the arcanist has, the consume spells ability which potentially adds yet more points to the arcane reservoir (on top of those the wizard needs to spend on Quick Study), and magical supremacy which is honestly pretty meh. The wizard gets Scribe Scroll, which is pretty good, and a series of bonus feats, which are also pretty good. Since Extra Arcanist Exploit is a feat, though not a wizard bonus feat, you can potentially make up some of the difference, too. Overall, the class features favor the arcanist but are pretty close to a wash; the arcanist will get more use out of their arcane reservoir, but the wizard will have more options since they could choose not to bother with Extra Arcanist Exploit and do something else with their feats if they wanted.
Now consider the rest of the time, when the wizard is a spell level ahead of the arcanist. That is a monumental advantage. It’s almost impossible to overstate how large an advantage having a spell of a spell level higher is. It easily doubles the wizard’s power, relative to the arcanist. The arcanist’s flexibility and greater usage of the arcane reservoir doesn’t come even close to that much of an advantage.
So even though 60% of the time, the arcanist is strictly superior, the other 40% of the time, the wizard is strictly superior—and by a far greater margin than the arcanist’s advantage on its levels. And, especially if you are starting at 3rd level or higher, and don’t expect to reach 19th level—which makes the split between them 50/50—things really very strongly start to favor the wizard.
Conclusion: wizard is the more powerful class
Pathfinder Society might matter here
Pathfinder Society specifies three sessions per level. Starting from 1st in Pathfinder Society means it will be six sessions until the wizard gets ahead, then three sessions favoring wizard, three sessions favoring arcanist, and so on. So consider,
||Time favoring arcanist
||Time favoring wizard
and so on. It will be a while before you really start to see the wizard pulling ahead. It isn’t really until 7th level (18 sessions in) that the wizard really looks substantially better.
Furthermore, Pathfinder Society tends to feature very low-optimization play, and arcanist and wizard are easily among the most powerful classes in the game. The arcanist is easier to play, and you have power to spare—you might prefer to play an arcanist just because you don’t need the power of the wizard and the arcanist is more convenient.
Doesn’t move the needle very much. They get summon monster spells on-time, which is impressive for the ⅔-casting summoner, but not so much for the off-by-1 arcanist. And it costs quite a few points out of the arcane reservoir to do it. Getting plane shift two spell levels early is a fairly big deal, as plane shift is a pretty good spell and two spell levels is a whole lot, but ultimately it doesn’t matter very much if you’ve got a cleric or oracle in the party. Getting planar ally at all is nice enough, but nothing stellar. Augury and contact other plane, again, nice, but nothing amazing. Contact other plane is an amazing spell, and you actually get it two levels before even a cleric, but it’s also just one per week which is pretty rough.
Occultist is a fine, balanced archetype, but arcanist needed an imbalanced one to overcome the wizard’s advantages.
School savant archetype
This is a good archetype; specializing in a school is good for a wizard and it’s good for an arcanist. And the exploiter wizard loses the opportunity to do so, which is a thing. But having more spells per day doesn’t make up for being a spell level behind nearly half of the time.
The opposition schools hurt a school savant more than they hurt a wizard, but it’s still really almost painless to just put Enchantment and Evocation in opposition. Sure, maybe you end up burning two prepared spells on contingency once in a while; no great loss.
So school savant is actually a better-than-neutral archetype, but not better enough.
Twilight sage archetype
Specializing in necromancy isn’t terribly painful, but it is a drawback. Consume life is, eh, it’s better than consume spells but only if you work for it, which might be annoying (as stated elsewhere, allowing you to use it on any unconscious targets, rather than only those who are actually dying, would be far better). The arcane barrier exploit is fairly good, but the twilight barrier isn’t especially better—you won’t be dealing much damage at all that way. Twilight transfer, well I mean, if you have a cleric or oracle in the party, again, they could just prepare breath of life (and then again, they might not bother, which shows how much it’s worthwhile to have it permanently).
Death’s release is weird. A 20th-level character shouldn’t plan on dying. Sure, it’s pretty effective if it happens in the right place (fight against the BBEG of the campaign or whatever), but ultimately I’d want to have something that I’m going to use more than just once, which is about as much as I expect this would get used.
I don’t hate the twilight sage, but I’m not blown away by it either. It’s probably a net negative, overall, from an optimization perspective. If you were going to focus on necromancy and take arcane barrier anyway, then it’s fine. Definitely doesn’t do anything to make the arcanist superior to the wizard.