Dragon Age: Inquisition - Before You Start
A subjective guide

• Highest DPS, highest single target damage. Can melt bosses in seconds on nightmare with some preparation.
• This DPS means you'll always want a rogue in your party. Let's say you play a warrior. The AI has no idea how to handle rogues (worse than mages), so you'll end up babysitting the rogue companion instead of playing your main character. If you play a rogue you don't have this problem. Leave the warriors to the AI.
• Can mix it up with close combat (dagger) or ranged (bows), although not on the fly. You'll need to respec.
• Most mobile, can jump around the field easily. There's even a mass effect style vanguard charge.
• The rogue specializations are very versatile. AOE-spamming zero cooldowns attack machine? Check. Blanket the field in mines? Check. Crazy single target burst damage that can one-shot bosses? Check. Tank like a warrior or freeze foes like a mage? You can do any (but not all) of these as a rogue. I took down a high dragon in ~10 seconds on the nightmare difficulty playing solo as a rogue, although that was after a lot of planning.

• Requires active control. Will get killed in seconds if you let AI handle your character. (Although see Survivability trap.)

• Only a couple of options for crowd control, even with the specializations.
• There's going to be lots of downtime in the first third of the game while you wait in stealth for your abilities to become available again. True for all classes but at least warriors and mages can continue to do basic attacks. Rogues will get killed if they do. (Mitigated somewhat by playing an archer.)

Ultimately this choice is a wash, but makes a big difference in the experience of the first third of the game. Also you can swap between the two at any time with a little gold.

In the early game, playing an archer is safer but less dynamic. (You only need to watch out for enemy archers.) The bursts are large, but cooldowns between bursts of damage are longer, you do a little less damage overall, and you will be just standing and shooting a fair bit. Some enemies jump around the field continuously, that's no trouble for an archer.

Playing a melee rogue is much faster paced and kinetic, you do more damage overall and flanking enemies is much easier. But the melee hitboxes are weird so you'll end up getting caught in stray swipes/swings and dying a lot. You have to chase mobile enemies around. You also can't afford to hand off control of your character to the AI and control one of the companions instead.

In the late game, both classes are pretty safe and hit like a truck. Archery is a lot more dynamic than before, you can spec like a "shotgun" archer who stays in close range and does a little melee on the side or vice-versa. The archer probably does more damage overall now. Choose based on the early experience description.

• Lots of crowd control skills
• Very, very flashy, especially on the frostbite engine. Uh, maybe this should be a CON:

• Has a specialization that turns you into an unkillable close combat tank (with a spirit sword and everything). The Knight Enchanter can go toe-to-toe with dragons solo. However this specialization is defensive so combat becomes slow and attritional.

• Other specializations are standard mage fare; you get some very powerful aoes. Can throw mooks around like puppets.

• Same as rogue: It's better you handle a mage than leave it to the companion AI. That said the rogue companion AI is the worst.

• Requires babysitting like the rogue. no chance of the AI using your spells efficiently.
• Might have trouble with bosses. Expect some of this:

• You'll have trouble if targeted by enemy archers. Can kill you easily if you're not careful, although not an issue from mid-game onwards (see Survivability trap).
• Two of your mage companions are interesting to quest with, there will be overlap with your skills.
• You'll never have enough skill slots. In inquisition you can only have 8 skills active at a time. This affects mages the most because their staff auto-attacks are pointless.

• Sword and shield warriors are set and forget. You can control the companion characters instead and mix it up.
• 2H warrior can do near rogue levels of damage but are about as durable (i.e. not very.)
• One specialization makes you pretty much invulnerable. Another ramps up damage significantly but loses chunks of health with each strike.
• Swinging a heavy axe feels much weightier than in Dragon Age 2. Satisfying thump.

• The best companion in the game for banter and interaction is a 2H warrior. If you're playing one too the party will be imbalanced and you might have trouble with fights.
• No crowd control to speak of.
• Not much mobility, although the play style is the inverse of the rogue: instead of pinballing between foes you can drag enemies to you.
• No ranged options, unlike rogue/mage.
• Fights will be more drawn out.
• The Survivability Trap: In general there's no reason to focus on survivability from mid-game onwards because you can easily craft stuff for rogues and mages that makes them as tanky as you want, with multiple layers of magical protection. Of course this comes at the cost of crafting stuff to do more damage instead. In any case this does take away the biggest advantage of playing warrior.