A 44 will be cheaper to shoot. 30-30 ammo typically sells for about $18-$20/ box, while 44 mags sell for about $10 more per box. But 30-30's come 20 rounds/box while 44's are 50 rounds/box so the price per round is less.
Most of the time a standard 336 will sell for less than an 1894, especially used. The 336 BL is more expensive, so that is probably a wash. Only you can decide which is worth the money.
There are more options for premium bullets in the 44 mag. Some of the hotter premium stuff is pretty powerful, but can be pricey. Not really needed unless you want to defend yourself from a grizzly. In that case I'd take the 44 over the 30-30 any day.
As a hunting round the 30-30 is more effective on deer/human size targets at longer ranges. If the shooter is up to it 200 yards is not out of the question. As a rule 30-30's tend to be more accurate. The 44's really start running out of gas, and accuracy after 100 yards. At shorter ranges 50-75 yards, especially on larger game such as bear I'd give the 44 the advantage.
30-30 is going to have far more range especially with LeverEvolution ammo.
The 30-30 is a better long range round, but the LeverEvolution ammo is more smoke and mirror than real performance. They cheat a little on their published ballistcs. Every other ammo maker shows a 100 yard zero with their 30-30 ammo and then show drops at various ranges. Hornady doesn't tell us what range they zero their LeverEvolution ammo. Only that it is 3" high at 100 yards, it is still hitting above your point of aim at 200 yards. This makes the 300 yard drop look real good. Their zero is probably 225-250 yards. Zero a conventional 30-30 bullet at 250 yards and the difference at 300 yards will not be that much different.
The 44 holds more rounds is lighter and will be faster for repeat shots. Lever actions in rifle calibers have such a long lever throw that they are not nearly as fast for aimed repeat shots as the legend would have you believe. Pistol caliber rifles have much shorter movement and less recoil which add's up to much faster shots. All the Hollywood cowboy shooters were using pistol caliber guns, not 30-30's.
Between these 2 I'd buy the 44. I don't like the BL. It is 1/2 lb heavier than the C or SS, 1.5 lbs heavier than the 44, has a shorter barrel,and holds 1 less round, 4 fewer than the 44. If the choice were between the 336C or 336SS, I might go the other way, especially if it were for an all around hunting rifle. But for hogs and a SHTF rifle I like the 44 better.