In nearly 3 years of living in Indo I've only been to Bali once soon to be twice. It is a cesspit if you are talking about Kuta, where dare I say it there are too many Aussies (and locals trying on Aussies accents and trying to pull you into shops. Got quite the shock when I spoke to them in Indonesian and told them I wan't Australian but from Eastern Indonesia).
There are plenty of other places to go in Bali outside of Kuta that can be far more enjoyable. Suzuki Jimny type things are cheap to rent and there are air-conditioned shuttle services plying routes across the island.
I haven't been to Phuket but have been to Koh Samui which I didn't think was all that great and mostly I've been told Phuket is a bit of a dump and a lot like Kuta. But at least Thailand understands tourism and things are a bit easier to do there. In Bali, even though it is Indonesia's premier tourist destination it is still a trial organising things for yourself. That said at this time of the year you can DIY on the cheap easily enough.
Booking.com is good, although usually slightly more expensive than Agoda, the advantage being it's only a reservation and you don't pay up front. Hotels.com is also a good site.
Perama Travel & Tour is the main shuttle company. Didn't use them last time but will probably use them on this trip.