Or do they have different speeds and accuracy?
In general, I'd say no.
They each have a different level of Mobility. This weight / mobility affects speed to bring up the weapon and aim / scope.
They also have different scopes and options that one player may feel is more suited to them over another.
So what one person feels may be "fastest" or "more accurate" another may find awful/slow/inaccurate.
You can tune each sniper rifle with the perks and proficiencies to allow you to aim more quickly and also to allow quicker movement WHILE aiming.
I've tested all the rifles and they all seem to react slightly different in speed to scope and aim.
You can sign up for Call of Duty Elite (free). It goes over each weapon's nuances and also gives tips for what perks and proficiencies to pair the weapons with for recommended performance.