I was just there in Thailand Feb. Phuket is very touristy and it is a beach version of Bangkok, there is allot of top side things to do. There beach reminds me of the beach of Majorca with all the people the on Patong beach. There are tons of clubs and plenty to do top side. Tons of shops if you have a lady companion going with you.
Tons of dive operations there. You can do a super sunday trip to phi phi island with sea bee's, with speed boat, that has 4 dive, with one being a night dive. They have very new equipment if you are renting and will discount if you bring your own gear. You can also take a day trip to the similan island, the diving there is fantastic, if you have a good day, you will see gaint manta's and whale shakes. On the day trips all food and drinks are provided. If you want a custom wetsuit you can go to hotwave phuket, and they can make on for you. The normal wetsuit for the summer is a 3mm shorty.
Koh Tao like Koh Samui has some touristy parts, but it is way more relaxing then Phuket. There are jungles unlike phuket, so you get nature also with koh tao. The diving in the gulf is not as nice as the andaman sea where the similian islands are. But there is still nice diving there. The water is a bit less green in the gulf the the andaman sea. You will find great food at a fantastic price also. If you eat where the locals eat, you are looking at 6 US dollars a day, and where the tourist go about 10-12 it is the same for phuket.
Since you are stay only for a short trip, phuket airport is only 12-20 minutes form the hotel area where patong and kata beach are. Koh Tao, you will have to fly to Koh Samui first and then take a boat trip to Koh Tao. Some Airlines fly directly to phuket, Koh Tao require transfer from bankok airport to Koh Samui, which is a insane air. There is more thing to do there then any other airport I have been in.
I my opinion the Khao Lak region of Thailand, which is 1 hour north of phuket on the mainland has the best diving, it is closest to the Similan Islands. This area is still rebuilding, since the tsunami heavily damage this area.
Thailand is awesome, my wife wants to go back next year. The food is fantastic, people are friendly. We were there for 2 weeks and the is so much more to see. You can not go wrong with either phuket or koh tao. I would try to see which location fits better for you short trip. PM me if you have any more question about thailand. PS Koh in thai means island,