Had both in a pistol. The .375 with 220 grain bullets was about like shooting a model 29 Smith with full bore 300 grain loads. The 270 grain bullet comes back about 1/3 again harder. This was in a barrel ported by SSK. (Jone's company). Muzzle would rise about 2-3 inches and recoil was straight back. The .309 was a rechambered .30-30 barrel. Recoil was not especially bad in any manner.
Case forming was not a problem for either, although I ran the .309 thru an intermediate sizer before going down to .30 cal.. Fireform loads were accurate enough for hunting if you so desired.
Sorry I don't have any experience with a rifle shooting these. Hope this helps a little.
If you are rechambering a 30-30 Contender Pistol barrel, you may want to try 30-30 Ackley Improved. It will do everything a .309JDJ will do with bullets up to and including 150 grains. The .309JDJ does handle the heavier bullets better (faster).
In the AI chambering you can shoot standard 30-30 ammo (usually fairly accurate), and instantly have the fire formed AIs. The recoil is also much less.