The first couple of times we visited Orlando we booked package deals staying in hotels on International Drive. As our girls got older and we found that we didn't particularly relish the thought of spending 2 or 3 weeks with them in one hotel room, we progressed to villas. Since then we have stayed in 10 different homes in Kissimmee and the available facilities have become increasingly amazing - huge flat screen tvs, homes with two or more master suites (avoids conflict over who gets the best room when travelling with more than one family), hot tub jacuzzis, poolside tvs and bars, stereo systems which can be piped throughout the home (including outside) and even home cinemas rooms! As I type, I am sitting in the games room (pool table, foosball, PS2) of the villa we are currently renting, taking advantage of the free internet access.
For me, the benefits of staying in a villa are space, privacy, our own pool, not having to eat out at every meal, cost:quality ratio and the ability to do a daily wash (meaning we can pack light and take home a suitcase full of clean clothes). There is nothing I look forward to more after the flight from the UK than relaxing in the jacuzzi with a glass of wine. We usually stay around west US192 which is as close to the Walt Disney World parks as some of its onsite hotels.
Of course, there are a few downsides - we love the whole hotel experience and, in Orlando, there is the added benefit to be gained from staying onsite at Disney or Universal. There is a lot to be said for being able to stroll down to the bar for a drink and then on to dinner without needing to worry about driving or taxis. Getting a taxi from the parks to your villa isn't a problem as you can direct the driver, but we've been late for dinner several times when we've tried to do it the other way around. We've found that the best bet is to find a local private hire firm (the prices are about the same).
We like to stay in brand new properties - everything is immaculate and the facilities tend to be better. However, development on each sub-division can carry on for several years, so you can find yourself living on a building site. The development we are currently staying at is almost complete, but there is a property being built next door but one and the builders have been hammering from 7am - 7pm

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We like to book directly with the property owners: that way we can choose the precise home and see photos/ask questions. It's also cheaper than booking through an agent. With each visit our requirements become more specific. My list currently includes an unoverlooked pool, a pool deck which gets the sun most of the day, two (or more) master suites, games room, PC with internet access, top of the range furninshings, and a hot tub. By sheer chance, all those I have used are UK owned. I have never come across any which are not managed locally, but you do need to ask the question. Needless to say, some management companies are better than others, but we have never had any issues which haven't been resolved quickly. In our experience, the biggest single problem has been with pool pumps and heat - I think we've probably had some sort of hiccough in at least half the homes we've rented. Clearly you need to be willing to accept the inherent risks of a private transaction, but I actually derive more comfort from dealing with an individual, who invariably is renting you their cherished dream vacation home, than with a business. There is a website where you can check the registered owner of any given property, but I'm not sure what kind of protection it gives you.