I have a 2010 Tournament 275 and absolutely love the boat (in fact - I couldn't be any happier with it). I have twin 150's and it is a great boat from every perspective.
When I ordered my 275, my wife actually asked me if I wanted the 307 and I considered it for a minute. As I was moving up from a Seaswirl Striper 2101 Dual Console, the increase from a 21' boat to a 27' boat was already quite substantial (not to mention going from a 3,000 lb boat to a 7,000 lb boat). Since the majority of the time I boat by myself, the 27' seemed fine and much easier to handle. In 20/20 hindsight, if the money were not a consideration (and it always is to some extent) and the fuel costs were not something to think about (the 275 gets reasonably good fuel economy) I would have bought the 307. I also like the fact that the 307 comes with a bow thruster (not sure if it's an option or standard but I would definitely get it).
If you are looking for an outstanding all-around day boat, the 307 (or 275) can't be beat. They are very, very seaworthy, extremely versatile, and of course made by Grady White (yes - I have drunk the Koolaid). Although I've only had my boat for one season, I put almost 200 hours on the boat and over 2,000 miles (just cruising around). With my old boat I went on 20 mile trips, on my Grady I'll take a 50 mile trip without a second thought. Everything you hear about Grady quality and customer service is true from my one year of experience (and I'm looking forward to my boat being launched for the 2011 season in 51 days - not that I'm counting or anything).
So while I can't tell you anything specifically about the 307 I can tell you that the 275 is an outstanding boat which leads me to believe that the 307 is even better. Of course it's longer, wider, heavier, and has more horsepower. What's not to love about that. If you can make the purchase work for you, I'm guessing that you will never have a second thought about having purchased that boat. It is unique in the industry as nobody makes a dual console that size in a mono-hull configuration.
I have to be honest and say that at this point, I don't have any negatives to share. Even though the price of a Grady is considered high, I think that they are great value boats for the money (in terms of quality, customer service, and resale value). I plan on owning my 275 for a long time (unless I hit the lottery in which case I'll buy a bigger Grady).
Sorry I can't be of more help about the 307. There are a number of great reviews on the Grady White website which may be of some help (and of course you should sea trial the boat). The best thing I did was to go the Grady White factory - the tour was amazing!