BeWitty
Lil-Rokslider
They don't make them in 338 anymore but they can be found used. I may have a lead on blued one....
You're really asking about two different machines meant for two different styles of hunting. This begs the question, where will you most likely hunt elk, in thick timber or open country? If it is the former, the .358 is the way to go (you already have a rifle that can reach out and touch 'em to certain degree and especially within your stated range parameters with the '08) and if it is the latter, the .300 is the way to go.
I have a Winchester Model 71 in .348 Winchester that was the predecessor to the .358 so they are ballistically similar except the .358 has maybe 50-100 more yards of effective range with the pointed bullets over the flat nose .348's.
Both are fine rifles within their style and type with nod probably going to the BLR since it is higher end manufacture for its type of rifle. I own both in different calibers and wouldn't hesitate to buy either again.
Reggie - I always used to shoot 175's and slid back to 140 all of last year, I did way too much load development with nothing else - I killed 3 elk this past fall, all with 140 Accubond or TTSX and I can say for myself that I'll not shoot elk with anything lighter than 160 from here out and if I can get that 175 Partition load to shoot again that is what I'll shoot - I shot a 6 pt bull at right at 200 yd and watched the entire caper go down - the bull died sure enough but he didn't know he was dead for way too long - a 160 7mm planted in the proper spot has so much more authority and a 175 even more, I hadn't put that much thought into it but when I hit an elk I want it to KNOW it's been hit - I'm actually seriously contemplating going back to a 338 Win Mag - a 225 "ANYTHING" is a heck of a lot more dramatic and a 200/210 does a heck of a job too - A lot of it boils down to personal opinion or preference because, as has been said before, "put any bullet into the right place ...." but also as said before "I want the animal to KNOW it's been hit" and those bullets START at 7mm / 160 and climb steeply from there (IMHO)
They don't make them in 338 anymore but they can be found used. I may have a lead on blued one....
I looked at one at SW in Loveland in 338 before Christmas. I opted for the 300 win mag. Adding a limb saver. I got the SW stainless fluted version.