I disagree that a car is always faster or easier. Far from it! It depends highly where you are going, and how you time it. If you are at Poly, for example, it's WAY easier to hop on the monorail to either MK or Epcot. Even with taking the buses, they often drop you off closer than parking, so you have to factor that into your timing.
PRO's
For us the biggest advantage is peace of mind. In an emergency - or mini emergency - you have quick transport off Disney. If someone gets sick say - Disney will have meds delivered to your resort, but y'know- there are some medical problems you just don't wnat to have to discuss with a total stranger. Disney does stock some stuff on property, but maybe not the brand you want or need.
It is very handy to have a car if you want to get from a resort to another resort, especially after a nice dinner, when most of the parks are closed (After dinner)
Although exceptionally clean, Disney transport is, more or less, PUBLIC transportation. If someone hasn't used deoderant, or a child is screaming, you smell/hear it.
CON's: For me, the biggest disadvantage is that driving around WDw can be a real pain inthe neck. I've done it quite a few times, and still, I have to re-orient myself every trip. Roads are not well marked. Getting lost sucks. The buses can take shortcuts that you can't - so again - sometimes the car is not as fast.
A second disadvantage is that you always need a designated driver. Usually ONE designated river the WHOLE trip (unless you pay the extra fees) That person has to be sober, awake, and able to navigate. I don't drink much, but it sure is nice when everyone gets to be part of the fun! Some of my family members are not good at navigating - so that means those who are always get stuck being the designated driver. If you are the driver, you have to focus on traffic and avoiding accidents.
Another diasadvantage - esp -at MK - is that if you park in the lots - you have to remember where you parked. Every night, some poor soul spends hours searching for their car. (more often several poor souls.)
Last trip, our rental car had problems. It took hours to get it remedied. The company DID NOT want to fix it or send us a replacement car. IT was miserable. The car we got, well, let's say the tow truck driver was an avid chain smoker - or at least the prior driver. Since it was brought to us, we couldn't exchange it for any other car.
Anything left in a car all day will be very hot all day. Chocolate, crayons melt. You are responsible.
I don't find it much hassle to get ona bus witha good unbrella stroller. Our family brings it in the room each night and packs it up for the next day (water, diapers, jackets). Taking a stroller on the monorail is a no brainer, you don't have to fold anything, much less fasten carseats. Taking a stroller on one of the parking lot trams is downright scary! Especially if you are by yourself and trying to also hold a sleeping child. Unloading as a solo adult is also scary since you have to get the stroller and child off before the tram pulls away - they don't wait very long for you to unload! A few seconds tops!
It's cool to arrive at MK via monorail, or Epcot via boat!
If you have need of motor-
scooter or something of the like, it can be MUCH harder to go by car. Many can't be compacted to even fit in a normal car. (On the flip,riding a bus with everyone staring may not be much fun either.)
If you have kids, you'll need carseats and seatbelts every trip.
Parking limitations at many resorts. Many deluxes only allow you a three hour pass, and only if you have a dining reservation. You can't park at Contemporary and hop to MK for the day.
Late at night, some of the remote parking lots can be quite lonely. Sure, you are probably always on camera.
Oh, one more - if you park at one park and take Disney transport to another - getting back to your car can be a challenge.
The DIsney bus drivers are often a hoot. They tell jokes, WDW trivia, and sometimes grant special treats. They are a real part of the magic.
We've done both. My ideal is a mix of both.