Warriors make for decent archers. They get +3 attack from being a Warrior, and up to another +12 attack from Lethal traits. This means that against unarmored targets using the most basic bow you can have anywhere from +25% normal damage to +167% normal damage on every attack, against the Assassin's chance of +100% to +200% damage on a critical hit, with the chance of critical hits being anywhere from 10% to 29% (barring possession of items which improve critical chance, or the presence of a Master at Arms Defender champion). With the end-game bows, the Assassin is unchanged, but the Warrior now does from +15% to +75% damage on regular attacks. If we call the Assassin's chance of a critical hit to be 3 out of 10 for 200% damage (full Vital Strike with 1 extra critical chance bonus), then the Assassin will on average attain 7 hits for 1x damage and 3 hits for 3x damage over every 10 attacks (assuming no misses), or 1.6 times normal damage. The Warrior, on the other hand, will average 10 hits for 1.75x damage over 10 attacks (again assuming no misses), or 1.75 times normal damage. However, this is against unarmored targets, or with the Assassin not having access to Shadow Strike and facing armored targets, and also assumes that the Assassin and Warrior both use a bow that doesn't get a significant fraction of its damage from something that bypasses armor. Note that the damage comparison applies equally well to any mostly-mundane weapon in the game, not just to bows (but remember that the exact values will change depending on the basic attack score of the weapon).
If, in addition to full Vital Strike, the Assassin also has some or all of the Shadow Strike abilities, figuring out whether the Warrior or the Assassin is better becomes a mess, because it's highly dependent on how much of the attack damage comes from things that get blocked by armor and by just how much armor you're facing. Similarly, even without Shadow Strike, it's a bit of a mess if the weapons in use have a significant fraction of their damage from things that bypass armor (e.g. 10 mundane damage + 10 poison damage). Worse, critical hits increase the damage dealt, but the basic damage before critical multiplier comes from the attack score of the weapon, so an Assassin who scores a critical hit using Weapon A will not necessarily do X times more damage than the Warrior who makes a regular attack against the same target while using Weapon A, because the Warrior's mundane attack score is higher, which means that the basic damage for the Warrior's attack is higher than the basic damage for the Assassin's attack.
Beyond that, there's also the marginally useful but situational Rain of Arrows ability for the Assassin, which is something that the Warrior cannot equal with a bow, and also the attack bonuses that the Assassin can gain if the target happens to be a Champion. It's also somewhat debatable whether the chance of a really big hit early is worth more than a higher average damage when fighting multi-figure units, because a big hit early can greatly reduce the amount of damage coming your way, but on the other hand it's also only a chance of doing so (and if your luck is like mine, you get the big hits against things that are nearly dead anyways, and the one or two damage hits against things that have piles of health left).