While puck-style discs obviously lack the marcel spring, many full-circle race discs are also built without a marcel. The advantages of not having a marcel are reduced inertia, quicker engagement/disengagement, and a much stronger carrier for the friction material.
You should check your bellhousing/flywheel for alignment/runout anytime you install a new clutch, but it's especially critical if you have a clutch disc without a marcel, since any misalignment in the system will cause the disc to grab first in some areas, rather than equally all around the disc, and clutch engagement will be anything but smooth (i.e., it will chatter, and with more aggressive friction materials, or a solid hub disc, the chattering will shake your teeth out).
To get around the marcel problem with a puck-style disc, several clutch manufacturers now offer full-circle discs that use several small friction pucks spaced evenly around the disc instead of a full circle of friction material. Obviously, the reduction in inertia is not as great as it is with a true puck disc, but it allows you to use heavier metallic friction materials on street setups without ending up with a disc that has excess inertia, or a horrible chattering problem.
Another method of clutch disc inertia reduction is the use of a solid hub. Typically, the factory clutches are designed to be as smooth as possible, so your grandmother could drive the car without complaint. As a result, the clutch disc is not directly splined onto the transmission input shaft, but rather uses a damper arrangement on the hub. The damper transfers the torque from the clutch disc to the splined hub through a bunch of coil springs mounted around the central hub. The stiffness of the springs in the damper are tuned to the level of isolation (shock and vibration reduction) desired. In the case of a factory clutch on a non-performance vehicle, the springs can be very soft.
Soft damper springs present the possibility of fully compressing the springs ("stacking" them) when asked to transmit large amounts of torque or during shock loading (i.e., the 6,000-rpm clutch dump). When compression springs are stacked, they become damaged and can fail. So we again have the possibility of a clutch flying apart at sonic velocities, reminding us why scattershields are necessary.
You might then think that the solid hub is the way to go for all performance applications. Well, maybe. The problem with the solid hub is the level of shock forces going into the rest of your drivetrain when the clutch "hits." If you're into high-rpm clutch dumps, a solid-hub disc will murder your trans, U-joints, rearend gears, and axles in short order. Trust me-been there, broke that.
To still allow a damped hub on a performance clutch application, manufacturers use much stiffer springs made from stronger materials and also encapsulate the entire spring in plastic to prevent the spring from ever stacking or coming apart in extreme cases (for drag-race setups).
As far as friction materials go, there are plenty out there for clutch discs, but they can generally be separated into two camps-organic and metallic, with things like Kevlar and carbon confusing the categories somewhat.
Way back when, asbestos was the common organic of choice, and it did an outstanding job balancing friction, wear, heat resistance, and cost. But as a result of the banning of asbestos in modern times, many other recipes have been developed. In general, the organics combine low cost with smooth engagement characteristics, minimal wear to flywheels and pressure plates, and reasonably low inertia. For stock and mildly modified applications, they are the best choice.

In addition, street-type clutch...

In addition, street-type clutch discs usually have a damper on the hub, so the power actually gets transmitted to the transmission input shaft through a set of springs. This takes a lot of the shock out of the clutch engagement, as well as reduces noise, vibration, and harshness (NVH). Race or high-performance clutches can also have sprung hubs, but the springs are much stiffer and stronger and are sometimes encapsulated in plastic to prevent them from bottoming out during abusive engagements (i.e., clutch dumps at high rpm).

For racing or high-performance...

For racing or high-performance applications, SFI-approved flywheels are always recommended. The unit at left is made of steel and weighs about 25 pounds. The one on the right is aluminum and weighs 14 pounds.

To reduce inertia, solid hub...

To reduce inertia, solid hub discs are often used in race applications. The disc facing material that can withstand the ultimate in abuse is the sintered iron. These discs can withstand tremendous amounts of slip without losing friction coefficient, or otherwise burning up from the heat. They can also be refaced and reused as long as you pay attention to the disc thickness and set your base clamp pressure accordingly.
There are problems with organics, however, when it comes to high-performance applications. First, the friction coefficients are generally low, which limits torque capacity. Second, the slip characteristics are not good for two reasons: 1. Slip creates heat, and the organics can cook out the resins when they get hot, so the friction facings get irreparably damaged once they're overheated (under extreme heat, they can also come apart); 2. The friction coefficient drops with increasing temperature, so if the disc slips a bit, gets hot, and loses friction coefficient, it will slip even more, get even hotter, and so on, as it quickly falls into a death spiral.
Bronze metallics used for clutch facings provide significantly more grip than organics and are therefore typically used in puck-style discs. Since metallics are much heavier than organics, the puck style keeps the disc inertia reasonable. Built without marcel springs, these discs have quick engagement characteristics and a quick, clean release, so these work well for quick shifts.
The downside to bronze metallics is additional wear on the flywheel and pressure plate due to the aggressive nature of the material. A puck-style disc without a marcel also means chattering is likely upon slow engagement (i.e., street driving). Like the organics, friction coefficient in metallics drops off with heat, so once the disc starts slipping and gets hot, it's only going to get worse.