It seems very odd that a PII450 would capture without dropping frames, but your P4 2.26G has problems. In my opinion, your PII450 probably ran as a Standard PC with APM (Advanced Power Managment) while your new PC runs as an ACPI (Advanced Configuration and Power Interface) PC. This is only a guess since I don't have your system to test. IRQ sharing via ACPI is probably the culprit in your case. The other possibility is that you don't have ATA Channel DMA drive access enabled. Enable DMA access first (In Windows 2000 via Control Panel, System properties, Hardware manager tab, Hardware, properties of ATA Controller, Primary and Secondary Channels, Advanced options tabs.)
You didn't specify an OS, but I will assume you are using 2000 or XP.
Under APM, you could force components to share IRQ's and infrequently if set to Auto in BIOS the board could assign multiple devices to the same IRQ's. With ACPI, there is a tendency to share IRQ's. If you have a video card and video capture on the same IRQ with your network or sound card, this may be the source of the problem.
To test if this is the cause, in the Control Panel, System properties, Hardware manager, disable every device like USB, NIC, sound, etc which uses the same IRQ as your Firewire 4300. Then attempt a video capture (without sound). If your Firewire card doesn't share the same IRQ with your video card or any other devices, you should be ok. In testing, I would also disable all USB controllers just for testing. If the capture works good after temporarily disabling devices, then I recommend either reinstalling the OS as APM or creating a separate hardware profile which does not enable the conflicting devices (for the System properties, Hardware tab, Hardware Profiles create a copy of the existing profile and name it Video Editing). Use this new profile whenever you want to capture video.
If ACPI IRQ sharing is the problem, I recommend reinstalling 2000/XP with APM and not ACPI. To do this you must change the BIOS to APM and reinstall the OS pressing either F5 or F6 at the setup prompt screen that asks if you have any SCSI device drivers.