I have both. My feeling is that both cartridges are deadly. The rifle is handy and light and has suitable firepower for killing practically anything up to a black bear in my opinion. I hand load both cartridges to make it more versitile for me. Both cartridges are versitile enough if your willing to pay for ammo if you can't reload.
If your recoil sensitive the .44 can be fired with .44 specials, which is a very mild cartridge fired from the rifle. The .44 is a hard hitting cartridge and my favorite standard loads hit 17" low at 200m with a 100m zero. A suitable range. Cartridges are less expensive than 30-30 and can be bought super hot for protection in dangerous game country (Although it is expensive)
The 30-30 is a tad flatter shooting and with a medium load hitting 9.5 inches low at 200 with my 150gr shots coming out at 2050fps. At 300 though the difference is much different, with the 30-30 pulling much farther ahead.
So if you want a rifle for shorter range firing my vote goes for the .44. Just because ammo is more available and cheaper and is found in decent loadings. The capacity is higher too.
I carry the 30-30 more honestly but I'm more interested in it's longer game. The .44 is an excellent cartridge though. If I can help you any let me know.