More recoil and slower velocity with any of the 140+gr .264 bullets that will match the 134gr ELDM ballistics.
The 130 ELDM starts faster than the 134, but is quickly overtaken due to the significantly lower BC. The 130TMK is even worse.
No grass growing under the 6.5WSM feet for sure, but seems a shame to overlook the 25 since you have the bullets already
The .257 134 ELDM has a .645 G1.
The .264 140 ELDM has a .646 G1.
The powder/recoil penalty for similar MV is marginal between these two and likely splitting hairs. 134 availability can also be hit or miss sometimes as well.
I'm not hating on the .25s, and my 25-284 is a sweet shooting rifle. The 25 creed, -06, -06AI, .257 WBY, etc..., are all great cartridges. However, the 6.5 is more versatile simply given the much larger catalog of quality heavy for caliber bullets, especially from 120-147gr.
From Hornady alone you have the 120 ELDM, 123 ELDM, 130 ELDM, 140 ELDM, 143 ELDX, and 147 ELDM. Berger, Sierra, and Nosler have several other good bullet options in this range as well.
Unfortunately, in this range today in .257 you have 5 choices-120 Grand Slam, 131 Sierra MK, 133 Berger, 134 ELDM, and 135 Berger.