I would get ASI on the Storm Driver & CTR on the Umbra. If you have an Umbra, you should know it Deals more Damage for no Status. All other Drivers(Excluding Prismatech) cause Status, Charged or no Charge.

You'll want to Inflict the Status as many Times as you want with a Status Driver, so ASI will Benefit this.

You'll want more Pure Power, so CTR is Essential for the Umbra/Prismatech Lines.

CTR for all drivers EXCEPT hail driver. The charge shot greatly increases your damage output when fighting crowds and increases the area where you can spread your status. I personally use the hail as a sniping gun to separate things like lumbers from scuttles so I would use the regular shots and thus need the ASI.

ASI for all drivers as it gives you more mobility if you are willing to adapt to the shot-pause-shot technique - also, for most time the charge attack will hit for only twice as much as a regular shot.

"im not even a gunner, and even i know using both shots of an alchemer can be risky... im not even a gunner, and even i know using both shots of an alchemer can be risky... "
Okay, sure, ASI helps you in spamming shots but thats not what you should use it for, you use it to be more mobile while poking the enemy with the shots

"And alchemer shot rhythm is hard to learn, the whole pause shoot thing is tedious and hard for anyone who doesn't main alchemers."
And how is that different from getting used to timing to the charge? Poor excuse.

Most of the time, the charge will hit for at least 8x as much as a regular shot, more if the stray bounces connect. Landing the charge attack into the side of your target is much much easier than landing the double damage regular shot. Plus, even if you miss, 4 regular shots come flying back so you're likely to get a bunch of damage in anyway.

You're grossly exaggerating the difficulty of aiming the charge shot. All you have to do is aim it to the side of your target. I estimate that 75% of the time where it's practical to be using the charge shot, I'll get it to clip. The regular shot is much less predictable and does not hit 3 targets very often, and only hits two sometimes.

And I thought the charge splits bounce twice, but if not then the charge does 6x.

I spam the charge shot whenever I do not need to be running around. I count that as many situations.

Edit: Look - all you have to do is not directly hit the monster to get the charge shot to work. The charge bounces are easier to land than the normal bounces because the split bullets don't start exactly where the big bullet landed; they start a little bit offset, making them very likely to be inside the target. It's almost easier to get the internal bounces than to fail. Against monsters that clump up a lot - Mecha Knights, Retrodes, Scuttlebots, Zombies, Jellies, I'll quite often land a charge shot between two monsters and kill them both at the same time if I'm soloing or in a party of 2. I use a Magma Driver with CTR Med and it's much quicker to kill by spamming the charge shot than using the regular attack. Obviously, I don't only use the charge shot against anything, since I need to move around and dodge stuff, and in tight situations involving things like Kats and Greavers, I won't use the charge shot much at all, but when I'm just kiting Zombies around and trying to DPS them down, CTR is a hell of a lot more useful.

This may be the most useless answer ever, but it depends on how you use the alchemer. If you charge it a lot, you want CTR. If you don't, you want ASI.

I personally go the damage route and split the difference on ASI/CTR with a CTR trinket and gun armor if I can (using vs monster type UVs). Generally I single-target with regular shots and go for the charge shots in crowds, which is intuitive and is the most reliable way to alchemize.

However (and this is really what makes alchemers so fun to use), regular shots can work well in crowds and charge shots can work well to single-target if you know the tricks. Perhaps even better than the other way around. When you see a crowd of enemies and you want to deal a lot of damage with regular shots, you'll want to aim at the spot in between two enemies who are very close to each other. Ideally, that one shot can hit six times (I have not yet gotten a handle on this technique). When you see a single enemy and you want to deal a lot of damage with a charge shot, you'll want to aim the charge at the side of the enemy (though if you aim too far you'll miss the enemy entirely; you want to hit it). If done properly, the charge shot and most of its splits will all hit the enemy, causing a lot of damage.

So if you've mastered one of these techniques, you may want to main either ASI or CTR and use the alchemer accordingly.

Aw man I have got to try that.

Welp. I'm sorry for taking the extra 3 seconds. Real sorry man.

From the bottom of my heart.

No need to be so serious, you missed the light hearted tone in my post.

By direct hit i mean the first hit which deals more than a regular shot, 1 hit, no bounces included, didn't mean to say the charge hits only with 1 big shot; by regular shots i meant the 4 split shots.

No gun armor currently increases gun CTR. ASI does not have huge effects on alchemers, it helps, but not as much as CTR.

While if I had to choose one over the other I'd go for ASI, the fact that it's much more practical to get ASI through other ways makes CTR preferable.