some years ago Dick Metcalf wrote that his go-anywhere, shoot any-size-Whitetail bullet for the .44 Mag' was a 210 gr' JHP, and he liked the Remington version as i remember. the 180 gr' bullet is used by some, but it loses momentum/energy/penetration more quickly than does the 210 gr' pill.
the 180 gr' bullet is also considered by some/many to be too light for good ignition of the better .44 Mag powders....velocity-wise.....such as H-110 or Win 296. even with a heavy crimp i'd still expect the 210 gr' bullet to provide better ignition. therefore, i'd only use it with something like Alliant's 2400 or Blue Dot, or IMR's Hi-Skor 800-X.
lastly, if hunting public land you need to anchor the deer so you can tag it, rather than risking a brawl with somebody who may want to tag it if it gets a good distance away from you before laying down. it isn't worth an argument; so hit the deer hard and put it down, i say, where you can be the first one to get to it.
good hunting to you,
ss'