If we have a car, we usually do a mix. But having done both, we often go without a car. Also, don't forget good ol' walking. Sometimes the shortest way to get from point a to point b at WDW is by foot.
A quick answer is ask CM what you should do in each case. Even as a veteran WDW traveler, I find myself asking sometimes when I have to make som unusual transfer. The CM's at WDW rarely steer me wrong. Bell services, and front desk CM's are great.
Often the answer is going to be subjective based on your preferences.
If we have no car, sometimes taxi is the best option. It might even be the best option in a few cases with car.
Generally, going to MK you are best taking WDW transportation, unless you are staying at a large mod and plan to leave at a peak time (just after parade, park closing, just after fireworks).
If monorail is the option, that's usually easiest and fastest. (unless it's late at night)
If you plan on having dinner at a resort, you may be better off driving. If you are eating at one of the Epcot deluxes and going to Ecpot that day - then you are best takign buses/walking from Epcot. If you are pairing MK with an Epcot resort - then the car is best. If you are having dinner at a resort- and using WDW transport to get back would be a two step process- your car is probably easiest. (or a taxi in that one direction)
The car is best for any hop that includes DTD and almost any hop that includes AK.
Anytime that you don't feel like having a designated driver - WDW transport is best. Driving also requires navigation. If you don't know your way around WDW, then sometimes the bus is better. Turns are marked, but it is easy to miss a turn. Some turns are not well marked - particuarly if you are trying to drive to a hotel. Miss a turn, and it might cost you 20minutes to loop around WDW. If you don't have a GPS, and aren't good at navigating, WDW tranport might be best. It's subjective, often driving is faster and you have control - but it's easy to sit and chat while waiting for a bus. Riding a bus can be relaxing. While you are onthe bus, you can use that time to take care of some things. A car may give you more privacy. But often taking the bus directly from one place to another is going to take slightly longer than driving, since you have to wait for the bus. but that also depends on where you park. Sometimes it's a hike to he resort parking lot (GF).
Weather is also always a factor, and how well you cope with traffic. WDW also has FREQUENT speed traps. Speeding tickets and DUI's can be a real downer. WDW has guests from all over the country and all over the world (many in unfamiliar rental cars). You'll see some really moronic driving in Orlando! Half the drivers leaving MCO don't know how to roll down the window when they get to the toll booth! The other half are local drivers who are annoyed by the morons...
There's also the idea of bringing stuff. With a car you can have stuff inthe trunk. A car means you have to use carseats and seatbelts. Disney buses are VERY clean, but you will see other guests. Sometimes other guests and Bus drivers are WONDERFUL, other times guests can be rude. To me, Disney buses are much nicer than real world buses, but they are still basically public transportation. There's always a good chance the bus will be standing room only; a car has guaranteed seating. but you also have to find your car in a VERY large parking lot, and if you want to hop between parks - getting to your car might not be fastest. Once we went to HS and hopped to Epcot. We left the car at HS. At the end of hte night, half of us took the bus (faster) and half of us went back to the car (slower).