My thoughts in this regard, now that I'm halfway through the upgrade trees for most classes:
here i am a bit disappointed. the most powerful class is the psi operative (i have two fully trained ones) followed by the grenadier.
It's an X-COM game - if psi power isn't all-dominating, something's wrong. As it is I'm dissatisfied with the way it's implemented for aliens, the associated AI, or both. Whenever I see a Sectoid raise a zombie I rejoice, since it means the Sectoid's wasted its turn as the zombie will die when it does next turn, and the zombies aren't the threats the XCOM versions are anyway. The psionic link Sectoids had in the first game was more dangerous. Similarly, mind control used to be something any player should dread, but now it just doesn't do anything - once the controller's dead, the unit doesn't even lose its action points. And as for panicking, while it's good that the medal system has gone so it's actually a meaningful part of the game, now that soldiers act more sensibly in terms of running for cover and hunkering down than they used to, and will never friendly fire, it's not as severe a penalty as it was.
I was thrilled when I learned originally that psi-power would be more ubiquitous in XCOM 2 than in XCOM 1, but ultimately XCOM handled it a lot better from what I've seen so far. Something is seriously wrong when Sectoids are less dangerous than the average ADVENT simply because psi attacks can mostly be ignored and they almost never use their plasma weapons (when they do, they're more dangerous, but time and again I've had a Sectoid flanking a soldier, or facing a wounded one, only to have it run off and animate a zombie).
2. Grenadier:
The best of the regular classes, insane area damage combined with very good single target damage and some control. The low aim can be offset by items and cover destruction with a liberal use of grenades.
From what I've seen so far the Grenadier is indeed the most versatile, and probably the best, class - the ability to equip with smoke shouldn't be underestimated either, since it allows the Grenadier to support at much longer range than the old Tactical class could (so far as I've seen flashbangs are basically worthless, as they seem to have less of an effect on alien accuracy than simply covering your units in smoke. While the additional effects of disorientation are okay, the AI seems less prone to clustering activated units than in XCOM 1 - in fact it seems specifically programmed to keep units at least one space beyond grenade range from one another - so you're going to protect against more attacks with smoke than with flashbangs).
My favourite build:
Shredder, Suppression, Heavy Ordnance, Volatile Mix, Salvo, Rupture
Shredder shreds more armour depending on the weapon tier (3 armour for plasma weapons) and some late game enemies have a lot of armour (e.g. gatekeeper has 5). Salvo is insane because you can use a grenade and shoot (after the grenade has destroyed the cover) or use two grenades in one turn. Rupture is very good for the most dangerous enemies, you will need it. The best grenade is the acid bomb, because it leaves a 4 damage dot on enemies, which means that one acid bomb is usually enough to wipe an Advent squad. I highly recommend blue screen ammo (+5 damage against robotic enemies), an superior scope and expanded magazine for the weapon and a personal combat sim that grants aim (for +30 aim in total, i.e. at max. rank you will have 105 aim).
I haven't unlocked most of these, however don't discount Demolition - I reserve suppression for units that - at that point - have higher accuracy, or weapons with scopes, but being able to demolish cover without expending a grenade (which, in any case, won't always clear heavy cover) is as useful now as it was for mechs in EW.
3. Ranger
The Ranger is good for advanced scouting and incredible burst damage, however i don't think you should have more than 1 ranger on a mission because they lack crowd control, area damage and ranged aim.
My favourite build:
Phantom, Shadow Step, Run and Gun, Implacable, Untouchable, Rapid Fire
Phantom is essential if you want to keep an advanced scout for the mission on all missions, even on missions where the rest of your squad starts revealed, the rest is fairly self explanatory. Make sure to use Talon Rounds and a Superior Laser Sight for 100%+ crit chance in close quarters. I don't use swords because Phantom is that good.
I think Rangers probably have the best-balanced set of options, in that most points on the tree offer competitive choices (though it's a shame that Phantom competes with Blademaster - Blademaster is okay, as long as you're careful and avoiding using the sword attack as a first resort and so suiciding your Ranger, but Phantom is as you say basically essential). I don't particularly favour Shadow Step + Phantom since it's often a bit redundant - I've had missions where I can keep the ranger in cover long enough to evade overwatching enemies, and I'd rather let him Shadow Strike.
4. Specialist
This class is noteable worse then the classes above. I usually bring a Specialist for ranged hacking and that is it. Everything a specialist can do, other classes can do better.
At least to the point I've reached (Lt.), this isn't true at all. The mechs and turrets I've faced aren't that formidable, but it's still valuable to shut them down for free. Combat GREMLINS either outright kill small robotic targets (and presumably do more when upgraded), and against anyone else act like a pistol shot (again, without upgrades) with 100% chance to hit and squadsight, which is solid for finishing off wounded enemies without needing to get within grenade range. The scanner is fine for evading blobs while concealed at the start of the mission, since it seems to point out locations across the map.
The downside I've seen to the Specialist is in the name - you can go down the medic path or the combat path, but there's no real incentive to mix-and-match, and what I've seen of the medic path is noticeably weaker than the combat path. The medikit is pretty much as effective when carried as when mounted on a GREMLIN, and if for whatever reason you don't want Haywire (or already have a combat operative), I can see taking the buff that removes unconsciousness, panic etc. and just taking the combat path for everything else.
Plus hacking is no minor bonus a lot of the time - often it's a way to get free strategic advantages (though most of the 'this soldier...' stuff is irrelevant since the Specialist shouldn't usually be on the front line). The Specialist above all seems to be the one class that can do things no other class can do better, from a 100% chance to effectively one-shot robotic units to getting free long-range damage to hacking. In a 5 or 6 man team, the Specialist and the Grenadier are the only classes I'd consider doubling up on (psi notwithstanding as I haven't unlocked those yet due to bad luck in rolling my first scientist).
5. Sharpshooter
Just a terrible class. The Sniper line is just too inflexible and slow, because a sniper rifle requires 2 action points to shoot. Even when you are in a good position the damage is nothing spectacular. The gun slinger line has a lot of flexibility but the damage falls off dramatically later on (although there are some good combinations, e.g. fan fire + rupture). The main problem is that besides damage he brings nothing to the table. If sniper rifles would only require one action point i would put this class next to the ranger.
I haven't tried going the gunslinger route, and snipers are still annoyingly inflexible without even having the default accuracy buffs they had in XCOM 1. Nevertheless I tend to want one, because squadsight allows me to concentrate fire so much more effectively (and works with phantom Rangers to pick off targets in non-activated blobs). Sniper rifles seem the best weapons to upgrade with the executioner module. I've tried running double snipers and have been unimpressed - this is definitely not XCOM's all-conquering sniper, but as a specialist role soldier I'd rank it about with the Ranger (i.e. below the Grenadier and comparable with or more likely below the Specialist).