My personal experience with Firewire on PC was easy. I used Win XP, a motherboard (A8N-SLI) with built in ports and a Sony DV-8 Camera.
Windows picks up the camera and could actually display a stream from the camera without running any video editing software.
Each camera would be seen as a separate device and all the video capture software I have ever used allows you to select from the range of available cameras or video inputs.
For editing I used Pinnacle, Windows Movie Maker and various ULead products.
The only issue I ever properly had was a Camera not being picked up by Windows 7 correctly - it would detect something but not a camera. It turned out the cable was faulty.
For Amiga, there appears to be MorphOS driver on Aminet
http://aminet.net/driver/other/Helios_0.4-svn_r560.lha. I don;t know what this is for exactly but connecting things require a driver for the actual input device e.g. the firewire port, and another driver for the device you connect to it, just like USB.
All of the expansion cards I can see for Firewire are PCI or Cardbus so plugging into a standard classic Amiga isn't possible and there wouldn't be enough speed to use the camera effectively.
