Ldsh_Tanker,
i am a new owner of a used Japan 340 Weatherby too. welcome. i am still getting use to it, dialing in loads, etc. wish it was going quicker but too much work, not enough play. anyway, i am finding that my 340 Wby is about as much gun as i have learned to shoot well yet, as far as recoil level. it's got a 26" tube and is not braked. i believe all 338-378s were braked but could be wrong. i dislike brakes tremendously as i've suffered enough hearing loss due to my ignorance as a youth. even with plugs and muffs, you cannot get the muzzle blast dB level down enough to prevent hearing damage every time you pull the trigger. So i won't use a muzzle brake. now whether or not the 338-378 is "shootable" without the brake i don't think i've seen much on the forum in that regards. my 340 is near my upper end for being able to shoot with any kind of precision, for the given recoil. of course i'm sure there are those that could shoot a 338-378 with precision and without the brake. as BB340 said, though, you'll likely have enough gun with the 340 for moose. i'm thinking out to 400m if you can shoot with precision that far. not sure if you're neck of the woods would accommodate shots that far. i suspect the 338-378 might add 100m to that. those ranges being estimates with assumed bullet impact velocity. you need to hit with enough speed to ensure good bullet expansion. if you're likely to see 500m shots available for moose in your part of the woods, than the 338-378 will have good bullet velocity at that range, given that you can shoot it well enough to make use of that power and range. if the ranges will be closer, then the 340 will likely suffice just fine, will have less barrel wear (mostly less throat erosion) per shot, and will be easier on your hearing. both are likely great. i am getting quite impressed with my 340. i've not shot a 338-378 however, so can't give you an apples to apples comparison. i'm sure you'll like either one, just don't underestimate hearing loss. you will have regrets. i do.
-tdbru