Ok, so I tested the RoF/minute of alchemical repeating heavy xbows (AL) against Needle (Ne), with Armor of Speed, Haste, and nothing. This is what I found.

No boost:

AL: 105, sometimes 108 (probably one or the other is my human error; they were in equal number)
Ne: 117

Armor of Speed:

AL: 117
Ne: 117

Haste:

AL: 114
Ne: 117

Interpretation:

Haste, as noted before, isn't as useful an effect on repeating xbows as AoS. It's good for run speed, though.

For some reason, AoS, which is stated to give a +15% alacrity bonus, equates to Needle's +20% alacrity bonus in my tests. Admittedly, I only did about 10 tests each, for one minute, and I am far from perfect, so there could be some error. If my test is correct, though, how ... disappointing - I mean, why bother putting this 20% alacrity bonus, when it's the highest such in the game, on the most sought after repeater in the game, if it adds nothing?

If you don't have Needle, or some alacrity boost, use Armor of Speed. I don't have a quiver of alacrity, but it would be nice to compare Needle's firing rate to that with a non-Needle xbow.

So, use Haste for the run speed, AoS for the boost to damage output. If you're good at twitch firing, you can ignore my advice since you'll reach 120 bolts/second regardless and it's likely the speed boosts will just interfere with your timing.

[methodology: using stoneskin's timer, I noted the number of quarrels in my quiver, and placed it on a hotbar, and pushed the attack button for one minute. I continued the test up until the last second of the minute and regardless of whether the xbow required reloading at the beginning. I discarded one outlier that was off by 12 bolts - it came in at 96 for reasons I don't understand - w/no boosts]