Think it depends on how much you want to do the theme parks - we would never rent a villa as the kids just want to be in the parks every day, so we do first stage in a Disney hotel, then second stage in a Universal one. Transport from Disney hotels to parks is fantastic, Universal you can walk from them all really quickly.
We never hire a car because the different insurance costs can really add up - cheaper to just take taxi if you do go anywhere else.
All depends on what you like as a family though - we could never do each Universal park in a day each (even with the fast passes you get staying on site), and that's with days where we start when they open and leave at kicking out time!
Time of year will affect things too - if you go at quieter times, less queues so that might determine where you stay and for how long.
So, in summary, we've gone for Disney and Universal hotels each time (apart from once when we booked late and stayed at non-theme-park hotel - hated it).
We get 10 day Hopper for Disney (you can go between parks so, for example, Animal Kingdom during day, Magic Kingdom at night) , 5 day Universal ticket.
Never hired a car - need a break from all that - but, when we have looked into it, seems you need to be very careful about insurance.
In recent years, have always booked it ourselves by doing flights etc separately. When we last went (January), we did get a quote from Virgin, they said they'd beat anything else. Priced it myself, came in £1,500 cheaper, they told me to grab it as there was no way they could match those prices.
Thinking of doing California next January though - so if anyone has any advice on that . . . . 