What is the rest of the build? The Gaming 3 has some new tech, such as M.2 and SATA Express, while the G45 probably has better components. Also the G45 has SLI, while the Gaming 3 does not, so if your using a Nvidia GPU you may want to go for the G45 so you can add a second GPU.
You're probably not going to use M.2, but if you have an SSD, SATA Express might sway you towards the Gaming 3.
If I had a Haswell chip, and no SSD, or if was was using Nvidia and planned to SLI i'd get the G45. But if I had a Haswell Refresh chip, i'd probably get the Gaming 3, just so I didn't have to mess around with the bios update before getting my CPU to work.