The two most common configurations are base/mobile (vehicle mounted), and portable (handheld). Generally for scanners the RF performance is about the same. The base/mobile style scanners generally have a better speaker (but usually benefit from an external speaker), and are more suitable for permanent mounting in a vehicle or at a desk. Portable scanners are generally smaller, easier to carry, and can run on batteries, but most have weak speakers and some are not as durable.
In many cases, scanner makers produce both a handheld and a base/mobile scanner model of the same design (they may delay the base/mobile version or release both at the same time). For the most part, both the handheld and base/mobile versions are circuitry wise the same radio with only the case, connection layout, and control layout different. Often they simply take the same circuit boards and put them into a portable case for one version and put them into a base/mobile case for the other version.
The sound from the speaker is often better in the base/mobile version generally due to the larger case (they may put in a larger speaker due to the extra space as well). The base/mobile doesn't have batteries (although many times you can see the battery level indicators on the display) so there's not an issue of setting fire to the scanner from overcharging (or improperly charging) the batteries in the scanner. The handheld version is easier to carry around while the base/mobile version is probably easier to mount in a car or desk, especially when using an external antenna.
It's probably a good idea if you're going to get both a portable and a base/mobile scanner to make them versions of the same basic design (like the GRE PSR-500 & PSR-600 would be) since you could easily program them identically (they both have the same features and use the same software) so you don't have to do things one way with the portable and another with the base/mobile.
Handheld equals take anywhere! It gives you a lot of flexibility in a small package. Even when used in the house a base usually ties you down to one room unless you wire the whole house. A portable can do room to room, not dependent on AC power.
I totally agree with trap5858 and his assessment on how much flexibility you have with the handheld type of scanner. I have been using my Uniden BCD396T since 2006 and really prefer it to the base/mobile type. Since it's battery powered, the movement from house to auto is quick and easy, and if you have a power outage at the house, you can still follow what's happening for as long as your batteries last.
I'm sure the larger speakers in the base/mobile unit provide better sound or more volume, but the smaller speaker in my 396 does a very good job for me - so it's probably just a matter of what you like.