The issue of tire size versus handling has been discussed extensively here so I'll try to sum it up.
Motorcycle tire sizes get larger from year-to-year so it's easy to think that bigger is better. However, chassis design development is the principal reason larger tires can be used to go fast, not the tire size by itself. So it's best to stay with the recommended tire and rim size on a stock bike.
The size of the tire is selected by each bike manufacturer during development testing of a new design. The manufacturer develops their chassis and suspension system components in combination with the tires in order to balance wear, traction, tread design, stability and handling design objectives. When you bought your bike, you paid for a lot of development and testing costs, so think carefully about what advice to take when making changes. It often will come down to individual riding styles and rider preference so be critically honest about your own riding capabilities and needs compared to others.
When you modify your bike you often need to reconsider your tire needs. More horsepower generally means a larger tire is needed. If you decide to put on a larger tire, then check the rim width specified by the manufacturer of the tire. You should consider the manufacturers recommendation for rim size as the starting point in evaluating what's best for your bike's handling and your riding style. Put too wide a tire on too narrow a rim and obviously you changing the manufacturer's intended profile so the tire becomes more or less round, perhaps making it wear out faster in the center, roll harder, or make it more difficult to get over in the corners. But that aside, you can safely fit several tire sizes to the same size rim. Another related issue to consider is front-to-rear mismatching of profiles and changes to the ride height. Be prepared for some design development of your own since changes to suspension settings will also be beneficial when used with larger tires.
Some tire profiles are more sensitive to rim width than others. Dunlop, for example, says that their 180 slick works fine with up to a 6.25 inch wide rim. In the past, both Michelin and Dunlop have stated that a 5.5 inch wheel is suitable for 160 through 180 tire widths. Different tire manufacturers specify different rim widths for their tires.
So the question might be – would you rather have more cornering grip along with a heavier turn-in and slightly lower top speed or have a quicker turn-in, less apex speed, but more speed on the straight? Getting the power and braking to the ground through the larger contact patch of a larger tire needs to be traded-off against the handling degradation experienced with a larger tire.
Ducati 748/9XX's come with 5.5 inch rims standard, although some 916's did come with 6.0 inch rims from the factory. In order to get the correct tire profile, the recommended street tire size for 5.5 inch rims specified by the Pirelli and Michelin is 180/55 and for 6.0 inch rims it's 190/50.
The outside diameter of both size tires is the same so a switch won't require a rear ride height adjustment. The important difference is that the 180 is a 55 section meaning that it's height is 55% of the width cross-section. The 190 is 50% of it's width. This means that the 55-section tire has a steeper profile, it's taller.
When you mount a 190 tire onto a 5.5 inch rim it's profile becomes slightly incorrect. The too-narrow rim forces the tire's outer edges inward into a tighter curve so that you can't use this part of the tire effectively. A correct tire profile creates a correctly-shaped road contact patch essential to optimum handling, better sidewall stability with less tire flex and, and better overall tire wear.
When developing the suspension for the 916, Ducati had World Superbike racing in mind so when they sold models for the street they decided to mount 190/50 tires to 5.5 inch rims, a good combination for stable handling. It's been pointed out that WSB Ducati's then used 19/67 race tires, roughly equivalent to a 190/60 road tire. So, we got the wide tire look without the quicker turn-in handling characteristics of the 60 section race tire.
In the 1995 916 owner's manual, Ducati specified the 180/55 as an "alternative" to the 190/50 and the bike's under-seat specification sticker also listed both sizes as recommended.
It wasn't too long before buyers figured out that switching from the 190/50 to the 180/55 gave a very noticeable change in cornering feel. The 180's, mainly because of their taller, steeper profile, turn-in much quicker and easier. So eventually the word spread, and everyone who has changed to the 180's has praised its positive effects on handling.
Keep in mind that, as any street tire wears, the center section wears down more rapidly than the sides, so a 55 section tire will drop to an equivalent 50 section over the life of the tire. Consequently, the turn-in handling gets sluggish as the tire looses profile. This partially explains the rejuvenating effect that a new set of tires will have on a bike's handling, and will give you an idea as to the magnitude of the effect of switching to a taller section tire.
Most of the perceived handling difference people are attributing to size effects is due to the fact that they have installed a brand new 180/55 tire in place of a worn 190/50 on a 5.5 inch rim.
A 180 tire is also slightly lighter. This will account for part of the subjective handling improvement experienced when moving from a 190 section tire. The weight difference between brands is greater, especially for the front tire. For example, 120/70 front Pirelli Supercorsa's (8 lbs. 6 oz.) Dunlop D207RR (10 lbs. 7 oz.) A 2 pound lighter tire will reduce rotational inertia by the same order of magnitude that you get when switching from an aluminum to a magnesium wheel.
The 190 size somewhat is stiffer because of the shorter profile. This results in increased grip and reduces the tire carcass flex (better feedback), making accelerating hard out of turns less scary. Also, if you reduce tire size, with the same horsepower you're going to stress the tire carcass more. This however hasn't been a problem, even with the most powerful street bike models.
The bottom line here is if you compare the handling of a NEW 180/55 mounted on a 5.5 inch rim back-to-back with a NEW 190/50 on a 6.0 inch rim you'll be hard pressed to tell the difference on a stock bike ridden on the street.