In the example you're describing, you won't deal 2x the damage; you'll hit faster (though not actually 2x faster because skills like Rapid Fire use certain breakpoints to determine how many units to fire per second based on your APS which doesn't scale intuitively) but each hit will also deal less damage per strike. We'd have to assume that in both weapons' cases they somehow dealt the same damage per strike for the weapon attacking faster to deal more DPS, which will not wind up being true in-game. though the proposition of damage per hit versus base attack rate currently does favor the faster attacking ranged weapons right now as it does not appear 2H crossbows are using the correct base damage at 70.
For the most part, you're correct in that it is largely a playstyle issue, however there are things that you have to keep in mind when it comes to Hatred and attack speed:
Your Hatred regen is not fully based on your generators. You have a base Hatred of 4 per second that is modified further by items on a per-second basis. Because this is a flat value, it actually favors slower attacks that are more efficient on a damage-per-Hatred ratio. That is, since a slower weapon will deal more damage per hit (and thus per point of Hatred spent), each point of Hatred has more value, and natural regeneration obviously is not affected by your attack speed.
This line of thinking applies to all the forms of Hatred regeneration DH has access to outside of our generators. Bat Companion (both the per-second passive and the 50 Hatred active), Blood Vengeance, Reaper's Wraps; all of these restore flat values based on factors outside of our attack speed, which means they inherently favor increasing your damage-per-Hatred efficiency.
One form of Hatred regeneration that is variable based on APS is Marked for Death - Mortal Enemy. However, this really only winds up being a wash and does not actually favor faster attacks in that any Hatred you can gain faster from this via APS will also be spent faster at a lesser per-Hatred efficiency.
A basic real-world example can show how the above forms of regeneration can have pretty noticeable effects on your gameplay. In the case of an ability like Strafe for example, you will burn through significantly more Hatred per second with a very high APS. It is easily possible to create a build where you can regenerate enough Hatred per second to use Strafe indefinitely with a slow APS but not be able to do the same with a high APS because you don't have enough natural regeneration per second to offset the difference in the rate spent.