Go with the 25-06.
The 6mmRem. and/or the 243Win. are essentially varmint cartridges which can be used for deer, but shouldn't as there are far better choices out there - including the 25-06.

The 25-06 (and 270Win.) is one of the finest long range antelope/deer rounds available. And, it's not too much for the larger varieties of varmints either (chucks & coyotes).
Much better selection of rifles available to choose from in 25-06 also (vs. 6mmRem.).
And, if you're limited to factory ammo, again the 25-06 has far more choices available.