As someone who also went from an original to the current, here's my answer:
Advantages:
1. Far more choices for content. Netflix, Hulu, The kajillion channels on there, etc. It's really wonderful.
2. AirPlay. I use AirPlay quite often; I even occasionally play games from my iMac on the big screen using it!
3. Legit HD. The old Apple TV did 720p at a low frame rate, while the new one does 1080p perfectly. It really does make a huge difference.
Disadvantages:
1. No local storage. If you're in the habit of loading your Apple TV up with content and taking it to a friend's house, you're out of luck with the new one. Next best option is to bring a laptop or iDevice with your content and AirPlay it.
2. No older hookups. It's HDMI and Optical Audio only. If you need Component video or RCA jacks for audio, you're out of luck.
Those would be the big ones that I noticed. I actually got around the lack of local storage in a fairly simple way -
I installed Leopard on my old Apple TV and am now using it as a media server for my home so that I don't need to leave any regular computers on. It gives me a small, quiet server as well as something to do with an older piece of tech besides stick it in the closet!
The old Apple TV can still be a wonderful little box - you just have to know its limitations and how to use its advantages.