Webster said:
I never had a 22-250 but I have seen several shooters struggling to work up loads. Some may shoot good some don't. A custom barrel helps a lot. I shoot a 6BR 1:14 twist. I suspect one advantage is all 6BRs shoot small groups. As for ability at distance I ran some numbers though Berger's ballistic program. I plugged in 250 yrd. for sight in.
Bullet drop and wind drift at 500yrds. 10 MPH wind 9 o'clock. I rounded to a whole number. Guess which one looks the best.
BC Velocity Drop Wind Drift (inches)
.22 55 gr. Berger Varmint bullet .210 3700 37 40
6BR 69 gr. Berger Varmint bullet .291 3350 35 29
6BR 88 gr. Berger Varmint Bullet .391 2950 38 24
I have no experience with the 6br, so I don't have anything useful to offer on that side of things. I have some experience with the 22-250, so I will throw what I know out there to muddy the waters a bit.
For the sake of comparison, I am going to use the numbers that Webster posted. Webster, I apologize in advance if it looks like I am picking on you. That is not my intent. I hope that you don't mind my using your examples.
There are some .224 bullets out there that have the potential to be game changers if you have the correct twist. If you are going to re-barrel your 22-250, forget the 14 twist. It is obsolete.
A 12 twist will allow you to shoot bullets like the 55g Sierra Blitzking (.271 bc), Berger 55g Match flat base (.262 bc) and especially the Hornady 53g VMAX (.290 bc). With the latest powders, all of these bullets can be driven very close to 3900fps with very good accuracy. At 22-250 velocities, all of these bullets will easily outperform the 69g Berger from a 6mm br as cited above. Even shooting factory Hornady Superformance ammo with the 50g VMAX (.242 bc) @ 4000fps, the 22-250 smokes BOTH 6br loads cited above by a wide margin in terms of trajectory, while staying even with the lighter of the two 6br loads in terms of wind drift. I am currently shooting a 22-250 with a 12 twist Shilen barrel and it shoots this Hornady load (along with everything else I've fed it) into one ragged hole.
In fact, even a lowly .223 with factory Hornady ammo, in terms of velocity, trajectory, and wind drift, will outperformthe 6br in the 69g Berger loading and run step for step with the 88g Berger loading (I am citing the Superformance 53g VMAX @ 3465 and the Superformance 75g BTHP @2930 respectively).
If you step up to an 8 twist in the 22-250, you can launch a 75g AMAX @ 3150ish. Plug those numbers into a ballsitic calculator and there is no contest. You won't even be playing the same sport.
As for accuracy issues with the 22-250, there are some potential pitfalls. IME and from comparing notes with other 22-250 shooters, for some reason most factory 22-250's have excessive freebore (mine was in the neighborhood of .250"). Excessive freebore and the crappy 14 twist in most factory rifles has a tendency to really kill its performance. Since you are preparing to install an aftermarket barrel, you have the opportunity to control the variables that cause accuracy problems in the 22-250. If you go with a good quality barrel, make sure the chamber is properly cut, and choose an appropriate twist, there is likely to be very little difference in accuracy between the 6br and the 22-250 under field conditions.
If barrel life is your #1 concern, then by all means, go 6br. If ballistic performance is what you want, the 22-250 walks all over the stated numbers for the 6br. Can you outperform the 22-250 with a 6mm? Absolutely! Go with a fast twist, heavier bullets, and a bigger case. But, the barrel life advantage goes away too.
All in all, for bullets in the 50-75g weight range, I think the 22-250 is pretty tough to beat.