I second Jason's statement about backing up FREQUENTLY, and want to expand on it.
The AVCHD format has its issues, whether its a hard drive, internal, or external flash based memory. They take great video, but editing and converting the video into something useable is processor intensive. On my HP dual core laptop it takes about 3 minutes to convert every minute of video from AVCHD into a standard resolution (720x480x30fps). While programs like Premiere Pro can handle the AVCHD video after some tinkering and less time consuming conversions, it still has to be converted some time.
At max resolution, my Canon Vixia HF100 gives me approximately 1 hour of record time per 8GB of disk space. That means that I can amass well over 10GB of data in a single chase, and transferring that to the computer can take upwards of 30 minutes with no conversion performed at all.
You need to make sure your computer is up to handling the digital video, especially if you hope to shoot in true 1080i. You should invest in an external hard drive, get AVS Video Encoder to do your conversions, and at least ensure your desktop at home is up to the task. I ended up building a portable desktop that can be put in the truck for editing video while chasing away from home.
The only problem as far as the actual video quality is that most of the AVCHD cameras under $1500 currently don't handle rapid motion very well. The compression artifacts become very visible very quickly with rapid contrast changes or when a large object (like a car) moves across the screen. I've never seen any problem with this at all in a weather setting except for the occassional lightning strike looking funky. They can be problematic for shooting news type video though. Investigate the particular model you're looking at carefully.
I love my HF100 and highly recommend it, but I really think chasers in particular (folks who aren't just recording their kids' birthday party in general) need to investigate thoroughly.