For power I don't have enough data on any narrow bars. I've been on 41s for most of the time I've had a powermeter and recently went to 42s. I feel slower in the sprint, feel uncomfortable, and in the only comparison I have I've been slower (race clip below's sprint is slower than last year's sprint).

Narrow bars help me feel like I can navigate traffic better, but honestly I can't say for sure if I wouldn't have gone through a gap with 42s vs 40s vs 44s for example. I race pretty conservatively - one of my personal rules is not to initiate contact to gain tactical advantage. Therefore I won't push or shove a rider out of the way, at least not intentionally. So although I've slammed into a rider accidentally as we both dove around a slower rider and ended up in the same piece of road, I won't reach out and push someone with my hand or head or whatever. I ride defensively to protect position, of course, and wider bars would actually help a little with that (and I hadn't thought of it until just now).

However I think that bike and body placement play a stronger role in gaining/holding position than just bar width. For example in all my examples the rider, when sitting square on the bike, is much wider than the bike. So how would narrow bars help? Well when I slip through a narrow gap I turn my shoulders to the side, making me a bit narrower.

When trying to hold position it's all about trying to keep a rider from taking the wheel from you. To hold the wheel you need to either place yourself between the rider in front and the wheel taker, if in single file. If side by side then it's about being more forward. In this latter situation I think wider bars would help a bit. In this race a fellow BFer (shovelhd) leads me out and two riders make half hearted attempts to take his wheel:

What "holding position" becomes is a battle to intimidate the other rider by not moving away when they get closer. I call this zone around your bars and front wheel "The Sphere", a personal space that when violated makes you feel really uncomfortable. By practicing contact side to side and fore-aft a rider can reduce their Sphere to near negligible size. This in turn allows them to hold a wheel even when pressured to move by another rider approaching closely.

As a general observation it's much, much easier to take a wheel than to hold a wheel.

Finally, watching the pros race on TV (I've never been at that level!), I don't think wider bars would help but I think narrower ones would. I've seen overhead footage of, say, Cavendish, holding his leadout train's wheel. btw he runs 42 cm bars, according to what I've seen. If his train gets derailed he's very good at finding his way to the front. He also will bob and weave on his bike to clear small gaps (so he'll turn his shoulders sideways to clear a gap, or tilt the bike away from him, effectively making it narrower), and generally speaking he doesn't initiate contact, either in the sprint or in the lead up to it. Of course he defends his position but there are sprints where he eases and loses his train rather than pushing and shoving his way through a hole that's closing.

The key is that he relies on his speed to win sprints. He's not like, say, Bettini, who got DQed for unsafe riding after winning a sprint in the Giro. Bettini is not as quick so he resorts to physically blocking other riders to try and defeat them. Sometimes that's okay, sometimes it's not.