I have a bike with 44 cm wide dropbars. I can ride all day on smooth roads but when it gets rough my shoulders hurt after 20 miles. I measured my shoulder width at the boney part just below the top and it measures 47 cm. So I figure I need wider bars. 46 cm are fairly easy to find and relatively inexpensive. 48's are rare and are pricey and the only one I've found (Nitto Noodle 177) requires a new stem to match it's clamp diameter. So we're looking at $140 just to try it out.

So as I'm inbetween two sizes which way would you go?

Since you have many miles on narrow bars I'd pick the 46cm one. But this comes from a rider who has issues with bars that are too wide... Andy.

Moved here from framebuilding.
I don't think handlebar width strongly influences comfort. I'm not going to say there is nothing you can do, but I don't think a wide handlebar is going to help that much with rough ground

I've always used the measurement from the socket "hole" inside your shoulder (arm/shoulder joint) to the other shoulder. That gives a much shorter distance. I agree with what has already been said that handlebar width influences comfort. You might look for another cause.

By the way, the wider the bar, the less aero you are. Most racers try to get as small as they can without hampering effective breathing.

Despite all the problems I used to have with my road bikes, I was pretty insensitive to handlebar width. When you think about it, handlebar width doesn't matter if you're riding on the tops. Are you sure your shoulder issues aren't a result of something else that's wrong - like drop or reach? Need to keep your elbows bent more?

I never liked bars that were too narrow, but back in the day they were all a lot narrower than today's bars. Saddle position changes the weight balance between butt and hands, that may be the only effective thing in this case

Too-narrow bars shouldn't make you feel uncomfortable on rough roads. The symptom of too-narrow bars is usually difficulty with deep breathing, opening the chest. Bar width is, from my understanding, a balance between the concerns of aerodynamic drag and those of deep breathing.

Maybe More pushups, musculature strengthening will help you hold up your body..
or the stem reach is too long..

The Noodles only come in 25.4 yes? You could use a shim but I think bars that wide are more intended for riders with loaded tourers who need the extra clearance and maybe leverage

Always like the wider bars myself- lets your lungs open up- Some thought them a liability in tight criteriums or big packs- but I still liked the leverage and strength position they gave me- if not racing the only reason I could ever think of for not using WIDE bars is riding up in stopped traffic- they may clip a side mirror a little easier.

Yes, I wonder about too much weight on the hands, or collapsed shoulders.

46cm one is a better

Whatever works for you specific condition. Realize that between drops, tops, hoods, mtb bars, aero bars (elbows 20 cm apart!), etc. the effective width of bars can vary widely...so to speak.