Wow, someone 6'3" needs *narrower* bars? Another unanswerable question, though there are guidelines: for road bikes, try shoulder with to begin.
For MTBs a little wider.
Seriously though. To get a starting point, sit on your bike (or even a chair if you can approximate your riding position/back angle); close your eyes and extend your arms forward to a neutral, "relaxed" position with elbows slightly bent (more so if you ride only gnarly stuff) and mimic holding the bars. Have a helper measure the outside width, and approximate grip (sweepback) angle, or to get the angle more simply, measure the forward/backward offset between inside & outside of hand rather than trying to measure degrees with a protractor (pretty much impossible). That can be converted to degrees with geometry, or much more easily drawn on paper and compared to bars in a shop.The position should feel effortless with no muscle tension. This is your baseline, or starting point. A bar that fits these measures should feel at the very worst "pretty good". If the position is truly neutral, it should feel like the bar almost isnt there. From there on out, it's all personal preference & riding style. Some people like narrower bars for less required movement to change direction, others like wider bars for more leverage. You upper body build will often influence this as well, though not always in the way one might think.
Bottom line is, start with a "neutral position bar" and trial-and-error your way to the perfect fit. Don't over-analyze it, even if you have a PhDs in biomechanics, mechanical engineering and physics. Riding will tell you more than any theory ever could.
__PS: Don't be afraid to experiment with bar configurations that you think you won't like or you feel are counterintuitive. You'll be surprised sometimes after you give it a chance. Again, ride more, think less!