Radial and conventional/axial master cylinders differ in the orientation of the piston relative to the handlebar and to the pull direction of the lever. The conventional design places the piston axis parallel to the handlebar and perpendicular to the lever pull direction. The radial design puts the piston axis parallel to the lever pull direction and perpendicular to the handlebar. Radial and axial master cylinders are functionally the same.
The main advantage of the radial design per se is that it moves the lever pivot point inward toward the centerline of the bike so that the same pull force develops a smaller moment about the connection point to the handlebar. This reduction in bending moment results in less flexing of the master cylinder housing. Any reduction in flexing of brake parts such as in the lever, MC housing, brake lines, calipers and caliper mounts add up to better brakes with better feel (modulation.) Also, aftermarket radial designs are generally stiffer than the OEM designs because they are machined from alloy billet material.
The main reason (other than for appearance and weight savings) that Ducati owners replace the factory set-up with a radial aftermarket unit is to obtain a different MC piston size (hydraulic ratio) and lever pivot point distance (mechanical ratio.) This allows you to selectively increase or decrease the amount of pull force required to develop the same force at the brake pads by using a larger or smaller MC piston diameter. This combined with a shorter or longer distance between the lever pivot point and the piston actuation link will shift the control to one of more power, or more sensitivity if you prefer.
Keep in mind however, changing your stock master cylinder to an aftermarket radial design will NOT give you more braking power to help you stop sooner.
A radial master cylinder with a different piston diameter and/or lever fulcrum-to-piston distance will only change the feel of the brakes at the lever. So keep in mind that Ducati chose a master cylinder size to give you the best modulation characteristics (feel, sensitivity and control) for your bike.
Good modulation means good feedback to the rider during a stop. A good braking system needs to establish the closest linear relationship possible between the force applied to the brake lever and the actual deceleration of the bike. Stopping power is technically easy to achieve, but achieving it along with good proportional braking response is more difficult. This, I feel, is the major factor influencing braking quality.
That’s not to say that the Ducati engineering department’s choice is best for all riders or riding conditions. The best choice for the track isn’t the best choice for the street.
Different riders have different preferences and we’re all adaptable. A rider is able to compensate for one performance drawback to gain an advantage with another. But again, it's situational dependent; a braking system that gives repeated stops from 150mph with the force application of one finger is not necessarily optimum for a 40mph panic stop in traffic. Even though a rider is adaptive to a braking system's general behavior doesn't mean that in an emergency that he'll use a light one-finger pull to stop.
So let’s move on to your choices.
First, there’s a different master cylinder size requirement for single rotor systems than for dual rotor systems. A dual rotor set-up has a lot more caliper pistons to move so a larger volume of hydraulic fluid has to be moved by the master cylinder piston.
Also, since different Ducati models have different size calipers and rotors you can’t always translate a recommended master cylinder size to another setup.
A master cylinder size designation is written AAxBB where AA is the diameter of the piston in mm, BB is the fulcrum-to-piston distance in mm.
The master cylinder piston diameter is chosen based on the number and size of the caliper pistons.
A fulcrum-to-piston distance affects two things: the amount of force needed at the lever, and the distance that the lever needs to be pulled through (to displace and compress the same amount of hydraulic fluid which in turns forces the caliper pistons against the rotor discs) to yield the SAME stopping power.
The Brembo aftermarket radial 16mm diameter master cylinders offer you the choice of a brake lever fulcrum-to-piston distance of either 16mm or 18mm. The stock Brembo lever has a 16mm dimension.
So your choice is either 16x16 or 16x18.
From the geometry, a 18mm lever will need to be pulled a 11% shorter distance than a 16mm lever but will at the same time require more lever force than a 16mm to stop the same distance.
The Brembo aftermarket radial 19mm diameter master cylinders offer you the choice of a brake lever fulcrum-to-piston distance of either 16mm, 18mm or 20mm. The stock lever is 16mm.
So your choice is either 19x16, 19x18 or 19x20.
19x16 (stock) requires the least lever effort but the longest pull distance for the best modulation.
19x18 requires 11% lighter pull and 11% longer pull distance than the 19x20 MC. More feel (better modulation characteristics) than the 19x20
19x20 requires the most lever force but the shortest pull. More like a trigger action.
Some riders think that this short-pull trigger action means that they have "better" brakes, but they don't - at least not for all riding conditions. What they do get is the same braking power with poorer modulation (feel) characteristics. Good for the track perhaps, but often dangerous on the street, especially in the wet. In an emergency, most of us have the instinct to grab a brake hard. So if you value a better feel, when choosing between the 19x18 and the 19x20 for the street, go for the 19X18. Better still, stay with Ducati’s choice, 19x16.
On the other hand, some prefer their lever hard.
So again, I'm not suggesting that every rider will have the same preference in a braking system's modulation characteristics. Depending on your preference (or need) you can have brakes with an initial vague feeling, a strong initial bite, or something in between. You can select pads that have better high temperature behavior. On a race bike you can select brake pad and rotor material that will survive a race without needing replacement, but on the street, materials need to be more durable and function under less severe braking conditions and more varied weather conditions.