It's a marketing trick to make people feel good, but it's meaningless for a Z68 chipset based motherboard. Buy the Gigabyte if it makes you feel safer, but both the Asus and the Gigabyte have the exact same Z68 chipset.
Edit: I checked a few Gigabyte Z68 motherboards on Newegg and I haven't found one that's B3 certified.
I agree with that 'Certified' 'stuff', and it makes 0 (zero) difference to 'us' what MOBO the OP purchases. We 'try' to keep an eye on what MOBO's are good, bad, best suited for a specific purpose(s), and if there's some tweaks that help the MOBO's run better.
Gigabyte, I hated most of their LGA 1366 lines, but I like most of their LGA 1155 lines - they improved quality to both their low to high-end lines. Gimmicky add-on features like 'USB TURBO' have backfired because it interferes with the GPU PCIe lanes (sharing) so you can go for x16 -> x8 if it's enabled; no so good if you have a GTX 570~590, etc. Fix Disable.
To a degree you are getting what you pay for, and there are MOBO's better suited for 'use' or have minimum requirements for example target OC or CF/SLI.
ASUS P67/Z68 Pro level or higher, Gigabyte UD5 or UD7 series - all are good.
To better help you, what are your requirements and what is your 'use' for this new build?