Hope he likes his new BLR! They are fun to own, carry, shoot and hunt with!
I own and hunt with both, and each has its own pros (and cons).
I have owned more Model 88s than I have BLRs over the years, and currently have 3: all rebarreled to other calibers; a 250 Savage, a 7mm-08 and a 338 Federal. (I also own Winchesters and Marlins and like them too! (But I tend to leave my Winchesters for use with open sights and scope my Marlins)
I currently still have my first BLR: a pre-81 in 358 WIn. I have used and carried this rifle more than any other over the years that I have owned it (22), although I have others that have actually taken more game. Not only do I hunt with it, I used it as my back up guiding rifle, saddle rifle, camp rifle, and back up archery hunting rifle. If I am trailing wounded game in the thick brush, whether mine, or others, this is my go to tracking rifle.
They are light and handy rifles that are easy to carry and quick to put into action.
I like having a spare magazine for quick reloads, although I usually do not need to. But it is comforting to know that I have it handy should I need it for any reason. I also have spares for my Model 88s. And this facilitates simpler, quicker loading and unloading when travelling in a vehicle, on a quad or in a sxs, or on horseback.
They are easy to mount scopes on, and I use QR style mounts so that I can take off to use the iron sights if needed or desired. Return to zero is reliable with the Leupolds. This is the same for the Model 88. (Not quite as available for the Model 94, but also available for the Marlins.)
Neither the BLR or Model 88 is simple for take take down and reassembly, but the BLR should be done by a gunsmith!
Neither has a great trigger, but with practice you can learn its individual characteristics and still perform decently with them. I have been able to consistently shoot 1" groups with my BLR, and recently achieved groups averaging almost 1/2".
The Model 88 is easier to make improvements with, but also recommend that you let a gunsmith do this if you are not experienced in this. With research, and talking to an old gunsmith in the States that has this knowledge, my local gunsmith did a fantastic job on my latest Model 88 in the 250 Savage, and it is greatly improved! I will be having him touch up the other two. When looking for a Model 88, I was advised by a gunsmith from California many years ago (no longer in business) that finding the rifles produced post '64 had the improved triggers and were much better in regards to overall performance. (Mine are from '65 and '66)
The stock design on the Model 88, as mentioned above, does little to reduce felt recoil. Installing a Decelerator or LimbSaver pad will make a difference. With the BLR being a fairly light lever rifle, if he should find the recoil of the 308 with 180 gr ammo to be a little stiff, the upgrade in the recoil pad will also be of benefit to him, by making the rifle shooting experience more pleasurable, and therefore improving his accuracy with it.
The Model 88s other advantage is the slightly longer barrel; 22" vs 20" for the BLR. This will give on average an increase in velocity of approximately 25-35 fps/inch with most ammunition. While not enough to make a difference for most shorter shooting distances (especially if hunting with open sights), should he need to reach out further e.g. 300 yards plus, it will flatten the trajectory some, and retain a little more energy for penetration and expansion of the bullet on game.