Sony Japan has a chart (in Japanese) that lists the differences between the A1J and HC1 here:
http://www.sony.jp/products/Professional/c_c/hdv/HVR-A1J/spec.html#2
Not a full list, but here are some highlights:
- Can record/play DVCAM in addition to HDV and DV (but will not do LP mode in DV)
- 480P component output
- Edge crop downconversion option (so you get full height but lose the edges on a 4:3 TV)
- XLR input with the adapter module. Also has noise reduction, channel selection, level adjustment, and manual gain
- Various timecode options
- Has a "full scan mode" that uses all of the CMOS chip's resolution when image stabilization is turned off
- No built-in flash (I think it has a normal accessory shoe where the flash would normally go since this is where the XLR adapter mounts)
- Assignable button
- Viewfinder is switchable between color/monochrome
- Can give reference marks for 4:3 and TV safe zone
- Adjustable curves for shot transition
- A few other picture settings
- Will not power off after 5 minutes
- Starts recording more quickly from standby mode
And it is generally rumored that the professional versions of their camcorders are built to take a little more beating and survive more wear and tear since they are generally purchased for professional use.