I own and have hunted Deer with .270 WIN (Remi 700); 30-06 SPFD (Savage 111FCNS); .50 Muzzleoader (TC Omega); 12 Guage Shotgun slug gun, and with a Ten Point Turbo HLX Crossbow, and if given the choice hands down I would use the centerfire rifles in all situations.
Yes a 50 cal Muzzleloader with drop a whitetail size deer like the Hammer of Thor if you get a heart or double lung shot, BUT accruacy as compared to a centerfire rifle is poor to say the least. A consistant experienced loader using premium Sabot's can reasonably hope, in my opinion at best have a 4" 3 shot group at 100 yards; whereas the same shooter would reasonably be expected to have sub MOA from a production CF Rifle shooting non premium factory ammo. We use Muzzleloaders and bows over here as it signicantly extends our Deer season. The reason that the various state Department's of Wildlife Management allow extended seasons for Muzzleloaders is that they recognize that the efficacy of Muzzleloaders are so much less than a CF rifle (due to both accuracy and followup chat capability deficiencies) that the 4 week typical muzzlelaoder season will result in the same number of filled deer tags as two week CF rifle season. This data comes about a each tag must not only record, when, where, but also how a deer was harvested when the paper tag is surrendered for the metal at the deer check station within 24 hours of kill.
Couple more issues to consider:
1. Because you must get in close with a Muzzleloader (75 yards or less), unless you are in a treestand (high seat for you guys), it can be dangerous so stalk in with a Muzzleloader, as you normally will have the 209 primer in place and there is no safety expect for half cock on nearly all muzzleloaders.
2. Muzzloaders really Kick HARD even with two pellets of 777 or pryodex, and if you go for the max load of 150 Grains (3 pellets); then you better make sure you are not using a tree or any fixed hard object to steady your shot, because it can increase the felt recoil a lot.
Bottom line, stick with CF Rifle's if at all possible, for both your safe and for the sake of your quarry.