Personally, I like Lilja barrels the best. BR or LRH. You can take 10 Lilja barrels, air guage and bore scope all 10 and 10 of 10 will be worth using. There are always a few rare turds that just will not shoot no matter how tight the tolerences but you will find those with EVERY single barrel maker and very few bad barrels period. If the maker inspects them and determines that the rifle was assembled properly and it still wont shoot, they will replace it.
There has been alot of discussion between cut vs button. The fact is when top makers are used you will see uniform groove and land demisions and uniform accurate twists.
FWIW, Shawn uses Hart for his 338 Edge builds. I think the reputation of his rifles says it all. Button barrels work period. IMHO Hart is on par with Lilja. One of my barrels is a Hart and another is a Lilja. Both are top notch with awesome accuracy. The RC 5R I had was also spectacular before it cooked. All 3 have shown .25 MOA capability and sometimes better.
As a side note, the Lilja and RC were both 300 RUM's. They both shot lights out when fresh. The Lilja however held up to the heat of the cartridge conciderably better than the RC.
My current 338 Edge barrel is an ABS which was originally a 30 cal RC 5R. After that cooked, I had ABS rebore it out to 338 caliber since it was a cut rifle barrel it was re-cut to the next size. It is still a cut rifle barrel even though it was re-cut by another outfit. It shoots very well and is holding up alot better than when it was a 300 RUM albiet I shoot one and let cool for 2-3 minutes. I dont know if that has anything to do with why it is holding up better or not. I know a gun smith who had the same barrel in the same caliber who had the exact same experience that I did. After a few hundred shots, he shorten it at the breach end and chambered it to a 300 WSM
and has not had any more trouble. My opinion is that a cut rifle barrel hold up fine on good balanced cartridges but suffers on very overbore calibers. Just my opinion talking here. If I had to do another all steel 338 Edge I would be going with a Hart or Lilja due to the 'hold up' better factor which maybe a myth but has been my experience. That MAY BE why alot of 338 shooter use Hart and Lilja barrels.