Both will work well. Obviously it would be best to use the one that shoots better. If they both shoot well, I'd prefer the Barnes due to the larger flat frontal area created after expansion versus the smaller rounded front and shed core of the partition. I've taken my fair share of animals in Alaska, including moose and grizz with TSX, TTSX, and LRX in various calibers and weights. They have worked very well every time. Swift A-frames are also outstanding big critter bullets and I favor them over the partition as well.
Using a 180gr TSX in a 300 win mag with a muzzle velocity around 3,000', I made a hasty shot on a bull moose at 11 yards when he dropped his head and lunged at me. The bullet went through his antler, entered his neck and was recovered under the hide on his opposite side shoulder. Even with passing through the antler, it still expanded in the neck then shed its petals thankfully dropping the moose on the spot.
Stay above 1,800 fps impact velocity on the Barnes and most bullets for expansion. More ideally, stay above 2,200 fps impact velocity on any bullet for better terminal performance due to the elasticity of flesh and vitals.