Sharing IRQ (Interrupt Request) can sometimes cause issues with bandwidth. It really depends on what is being shared.
System Information - Hardware resources - Conflicts/Sharing
If your Firewire controller is showing as sharing, what is it sharing with? On the same tree, you will see an entry for IRQ, where you can see all the IRQ assigments.
There's not a lot you can do to affect IRQ sharing in Windows, as Windows does the assigning. But, turning off unused devices in BIOS can cause assignments to shift around. So, for example if you turn off an unused serial or parallel port, all the IRQ assigments can shift and maybe elliminate a conflict.
If, for example, your Firewire controller is sharing IRQ with something that's busy, it could create conflicts. Something like a modem or LAN card, video card, etc. It's just something to rule out. Laptops have notoriously limited bandwidth on the PCI bus, which is where everything runs.
You might wind up changing the Firewire controller in hopes of getting one that plays nice with the external box.
To rule out issues with the drive and box, take it to another computer and test it.