Asking in general about mb's is like asking should I drive a Ford or a Chevy. There are good in both, but without a budget, you are just getting speculation and arguments.
Both have excellent reputation, and I have one of each in the house. I would say, of the two, the Gigabyte is more stable, all things considered, but it was a $159 MB, vs the $69 Asus cheapo, so you get what you pay for.
If you're serious about building your DAW machine, look into the GA-Z77 (only $100) with a fast i5 and some HyperX
Beast (or other fast) memory. If you need TB over firewire or USB 3.0 you'll pay
the premium. The Lynx PC card is around $600 and cheap versions still run around $400. AND I didn't quite understand this part of your question, as the card will plug INTO your PCIe slot on the mb. If you're using SATA 3 w/6.0 GB data xfer rate, and install adequate internal drives, your
standard firewire interface works very well. MOTU is well known to support mac first in its products, so the TB interface on their new stuff doesn't surprise me, as TB is mac.
Anyway, if you're building and want TB, maybe you should consider making
an i5 hackintosh. Others here can advise you on that process.