Looking to build an ar platform dmr style rifle, 6.5 grendel or 308 and why?

I would have to agree with Lord.Duffman. I have owned both. They are both well equipped to tackle medium range engagements with good accuracy, and the components for both are similarly priced for the most part. But, 6.5 Grendel allows you to stay with the smaller AR-15 platform rather than AR-10, saving you some money on magazines and a few other components like the BCG and receivers themselves. I have not encountered anything yet that my 308 will do that my Grendel cannot, minus beat up my shoulder after a few dozen rounds.

I would personally go with a 6.5 Grendel. It's a flat shooting, low recoil cartridge that can stretch out effectively when you need it to for anything within most DMR ranges. There is a growing amount of new brass available for reloading with its increased popularity. I would say the only downfall I have experienced is when loading bullets above about 130 grains, pressure signs can show up quickly if you load it a little too hot.