I just came back from Disney and once again I missed shots with my advanced point and shoot. I am upgrading to a DSLR which I know I should have done all along. I have narrowed my choices to the Sony Alpha 300 and the Nikon D60. I am leaning towards the Sony because I have an H-5 and H-50 now so my memory sticks are compatible. The Sony also has more inexpensive add on lenses. I have also heard really good things about the Nikon. Any advice from people who have either camera and can give me the pros and cons would be appreciated.
I've been in a similar situation as yours - having replaced my H5 which I loved with the A300 which I also love.
A few things I'd point out:
First, a DSLR will improve your chances with some missed shots compared to bridge-cams like the H-series, but it doesn't fix all that ails you. It's a combination of larger sensor, the right lenses, and your skill, that will make the photos better. Getting a DSLR will give you a bigger sensor...so one down. If you're willing to spend some money on the right lenses, you can fix problem 2...but don't expect to do that much better with the kit lenses. Though most DSLRs can shoot comfortably and relatively noise-free at ISO800 or more, while your P&S cams can only push to 400 reasonably...that's only one stop of sensitivity gained. Your H5 lens is F2.8-3.7...compared to most kit lenses that start no better than F3.5, and anything that will give you the zoom capability from those H series (or even anything close) is going to have a maximum aperture of around F6. So you lose 1-2 stops of sensitivity on aperture...and you're not going to get that 36-432mm optical range without spending around $1,200 and carrying a whole lot more weight and bulk. Just a forewarning in case you hadn't considered it! A DSLR is still a better tool for more photographic situations, and for action shots, night handhelds, and indoor high-ISO, it'll crush a P&S.
There are techniques and styles you can use with the H series cams to improve your results in some areas...the only areas you should genuinely have limitations in would be indoor low light, handheld night shooting, burst mode speed, and tracking focus/action shots. Handled correctly, the H5 can do most everything else extremely well.
Second...You can't really go wrong nowadays with any DSLR...so don't worry too much about brand. I'd strongly recommend handling your two choices, hold the cameras to your eye, see how the buttons fall to your fingers, and how comfortable the camera is to hold. As good as all cameras are, they are designed a bit different, and sometimes one brand's ergonomics just fit you perfectly.
Third - don't let the memory card thing sway your decision...the A300 does NOT take Memory sticks. It uses the common CF cards. You can get adapters to use Memory sticks in a CF slot, but truly there's no reason to. Memory is so cheap nowadays, you can pick up a 4GB Extreme III card for $30 or less in the SD format Nikon uses or the CF format Sony uses...and they'll be faster than your Memory cards anyway.
I went with the Sony A300 for a few primary reasons - 1. I liked their implementation of Live View...I use it rarely, but when I do, it's simple, doesn't slow down the shooting or focus speed at all, and can be switched back and forth easily with one switch. 2. I liked the ergonomics and feel of the camera, and found all the buttons' placement was easy to pick up and fairly instinctual. 3. I liked the lens options which I found priced nicely, and the in-body stabilization means that every lens I add, including old used Minolta lenses and low light primes, are stabilized. 4. The price was good.
I don't think you'll find any drastic differences between any of the DSLRs in the same class and price range. There might be a feature here, a slight edge there, but they're all pretty capable and similar, and all will have improvements over your H5 and H50. Feel free to check out my galleries - I've got lots of pics there from both the H5 and the A300 - the shots from the A300 are spread throughout many galleries, but also all copied to one main gallery called 'Introducing the A300'. I bought mine with the SAL 18-250 lens, which is a nice walkaround lens that comes close to equalling the range and flexibility of the H5...giving me an equivalent of 27mm to 375mm. I also use a Tamron 200-500 for the long-distance wildlife stuff, and an old Minolta 50mm F1.7 bought second-hand for low light work.
Hope that helps!