Racers
There are currently four types of racers. The first generation (and my first Mini-Z) is the MR-01. It has been around for several years and can still be a competitive racer. Like all of the Mini-Z's the steering is proportional. So when turning it behaves like a real car. A small turn of the steering wheel translates to a small deflection in the tires. If you have ever driven a really cheap RC car some of them only have 1-3 distinct turning positions. Any hobby quality RC car will have Propo steering.

Some of the distinct characteristics of the MR01 include a stacked battery configuration and a linked front suspension. It's a pretty good car but it has its limitations.
The second generation of racer is the MR02. Personally, I think this is still the fastest chassis even though there are 2 that have come after it. Significant improvements over the MR01 include an independent front suspension and a laydown battery configuration. Instead of stacking the batteries on top of each other on the sides of the chassis, all four AAA batteries are as low as they can be. This makes the car slightly wider but it handles much better because of the lowered CG. The Kyosho website does a good job of illustrating the differences.
The next generation is a hybrid of the MR01 and MR02...the MR015. It has the battery configuration of the MR01 but the suspension of the MR02. The MR015 and MR02 come in two motor configurations, MM (mid mount) and RM (rear mount) which determine which bodies you will be able to run. I won't go into details here but there are several threads on mini-zracer.com where you can get more information.
The All Wheel Drive (MA-010) is the latest chassis to come from Kyosho. It has independent suspension at all four wheels and even more exciting is that you have driving power at all four wheels. It hasn't been around for very long so it hasn't been able to upstage the MR02 as the premier racer but for drifting you can't beat it. All you need is a set of drift tires and you are ready to roll.

For more information on the AWD you can check out the Kyosho website.
Formula One
I think the F-1's may have the most "cult" status of the Mini-Z's. They are much more difficult to drive than the racers and it's a lot easier to break parts. They are slightly larger and require considerably more driving skill. Actually, I don't know that it's that much more difficult to break parts on the F1, I may be slightly biased. I used to race a very unforgiving track and the open wheel design left many drivers with broken steering knuckles. It doesn't happen as much with RCP (actually I haven't had it happen yet) but they can be fragile. You certainly can't bash around the kitchen floor or outside with the F-1.

Overland
The overland is the SUV of the Mini-Z world. The tires and suspension are a little bigger than the racers and they can handle some minor outside driving. I wouldn't recommend a lot of serious jumping without preparing to replace some of the stock plastic with a little bit of alloy. These can be just as fun as the racers with the option to turn them into suspension modified rock crawlers. For more information on the OL's, browse the forums.

Mini Z Monster
The Monster shares the same chassis as an overland. Until recently the monster was the only Mini-Z that I had not driven. Although the main chassis is the same, some of the drivetrain parts are different. As of the writing of this breakdown, I haven't really inspected the two chassis together.

Other Resources:
Mini-Z Time is a great website for finding more information. There are videos so you can see all of the different chassis in action as well as a car lineup where you can see all of the Mini-Z bodies grouped by manufacturer and chassis.
If you are looking to get into Mini-Z's you can find all of the chassis above and hopup parts at the Mini-Z racer.com shop. If you are trying to get in for a little cheaper than a new readyset, you can sometimes find some forum members selling cars in the miscellaneous discussion thread. The forums are also a great place to ask questions to fill in anything that may not have been answered here.
Enjoy...
