OK, I will bite.
Hardtail: The most complext car to make repeat. This is all done in tires, gearing and converter
Slipjoint: Hardtail car that has spots in the chassis the allows certain points to moved or "slip" on the tubes.
4-link: Rear suspension the consist of 2 shocks, wishbone, anti-roll but ultimately is independent on each side of the rear end housing
Swingarm: This is like your 4-link however the bottom 2 four link bars will be connected to each other with a K-bar or X bar that does not allow the bottom bars to move independent of each other.
Monoshock: Only 1 shock and is found a more typical set up with a swingarm suspension.
Dual Shock: 2 shocks which is most commonly used on a 4-link car as well as some swingarm cars.
A 4-link or swingarm car allows for more error to be made in tire pressures and converter choices. It will allow you to adjust for track conditions easily. You have a tunable chassis with the suspension. With the hardtail/slip joint you can either change tire pressures, converters or gears to adjust to track conditions.
Hardtail/slipjoint cars have a tendency to bounce when trying to slow from a burnout or at the finish line when you lift. A 4-link car will not do this and for that reason can be much easier for someone to drive.
If I was going to bracket race or super comp race or even a top dragster race I want suspension on my car. I want the car to be smooth off the line, smooth when the stop comes off and smooth when I am racing the finish line. Heck, Marco Abruzzi is going 6.70's on motor only with a monoshock swingarm car. Plenty of guys deep in the 6's with suspension.
Here is where the down fall of suspension comes into play...weight!!! A 4-link car is heavier than a hardtail/slipjoint car. So if you don't want to spray hard or have the coin for a monster of a motor, you will be able to go faster for a smaller price with the hardtail/slipjoint car.