Hi Terry, GREAT question!
The 6.5mm vs. the 6mm is obviously bore diameter; .264” vs. .243”. That being said, the 6mm Creedmoor will shoot the lighter weight bullets faster. While speed isn’t everything in shooting it sure helps as far as holdover and windage when shooting longer distances.
The 6.5 mm’s have some of the best bullets ever manufactured. They are long for weight culminating in VERY high Sectional Density and BC’s. The higher Ballistic Coefficient the flatter shooting and wind bucking those bullets will be.
It all depends on what you want to do with the cartridge. Both are awesome target rounds as well as great hunting rounds. If you want something with a little more versatility personally I would lean toward the 6.5mm Creedmoor as living out west we hunt elk and the 6.5 Creedmoor’s heavier bullets would offer more penetration at range. One thing to consider is barrel life, the 6mm Creedmoor is a little overbore and depending on your shooting habits “could” wear out the barrel quicker.
Here is a link to a VERY informative site that talks a lot about both Creedmoor cartridges. Either way you go both are AWESOME performing rounds… Hope this helps…
http://precisionrifleblog.com/2017/02/16/long-range-calibers-cartridges-what-the-pros-use/

There are more good 6.5 caliber bullets available. The 6.5 caliber has gained quite a reputation over the past 120 years as a target and hunting round that has no match for the recoil sensitive shooter and it is easy on barrels so the equipment will last longer. This rebirth of 6.5's is just what we knew in the 1960's and 70's with the 6.5-06 and 6.5 Redding. The 6mm's never had the following of the 6.5's because even though you get a bit more velocity they do not perform as well.