Tough choice, there probably is not wrong answer here. You weren't very specific on what you need this rifle to do, how much you plan to shoot, what you intend to "wack 'n' stack" with it etc.
I have a 6.5wsm, 7mm SAUM & 7.82 Patriot (300 short mag). The 6.5 & 300 have stacked up hundreds of pounds of meat, both kill well. (no kills on the 7mm yet).
The 300 has more brass (cajones) from a pure killing power standpoint (I think). The 6.5 is a finess cartridge I feel, a little more accurate, way easier on the shoulder & quite a bit flatter shooting.
It you're a "one gun" type of dude, don't build a 6.5. Short barrel life coupled with a very high Fun Factor can lead to a rebarrel/setback fairly quick like
The 270 cal Matrix have me intrigued but not enough to build one.
Even though I voted for the fun factor of the 6.5, the 300 is one tough cookie to beat.