From an efficiency standpoint, which one wins? Assuming standard MF gear and nothing super expensive for either.

Hdin: most expensive item will be enigma
Sorc: most expensive item will be infinity
(Assume no/low griff, no/low crescent)

I think cost is similar, which one would be better for mf?

Sorc is the most efficient u don't even need infinity, just farm AT as blizzard.

hammerdin with shako

run cs 24/7

Shako

With your budget the Hammerdin will be better. A strong pvm lite sorc wants crescent, infinity and enigma which leaves you with no resists and you need to pay for @res charms too which will blow the budget by a lot.

Hammerdin with ladder runewords is the best choice for autists.