Grumpy - both of these cartridges are a heck of a lot of gun for deer. But both should perform well on hogs. IMO I would probably opt for the .45-70 even though the 375 is also a good choice. You may have trouble finding ammo for the 375 JDJ.
I've taken 3 bear with my .45-70 Guide Gun using 300 gr HPs and it has performed admirably. The first 2 were with factory ammo and the last one was with handloaded ammo.