Pressure being equal, the 6.5-284 due to its larger case capacity is going to shoot a little faster, 75-100fps faster give or take.
You can get Lapua brass for all three so neither has any advantage there.
Biggest difference is the 6.5 Creed and 260 Rem can be maxed out to their fullest in a short action.
For me, I'd never do a straight 6.5-06 over a 6.5-284, the 6.5-284 is just to darn easy, has better brass, unless you neck down Lapua 30-06 brass, and they're virtually ballistic twins, but if you want to go 6.5-06AI, then there is a little more velocity to be gained. I have both a 6.5-284 and a 6.5-06AI. The 6.5-06AI will shoot the 140 Bergers about 50-75fps faster than my 6.5-284 but there is much more work and expense involved in the 6.5-06AI.
I'm a big fan of the 6.5-284 but with Lapua now offering 260Rem and 6.5 Creed brass, they're hard to overlook.