I'm partial to muzzleloaders myself, but here's my opinion on the advantages/disadantages:

.50 cal ML

Advantages: Most of the time more accurate than a 12 gauge slug gun, even if the 12 has a rifled barrel
Less recoil
Cheaper to shoot (over the long run)
More fun (in my opinion)
A much wider variety of bullets to choose from (many various saboted rounds, conicals, etc.)
Better deer killing power with the right load - my experience has been with a proper load & bullet,
deer tend to drop instantly with a well-placed shot

Disadvantages: You only have 1 shot
Longer time to reload

If you were doing a lot of deer drives, I would lean towards the 12 gauge - you'll have the option of fast follow-up shots which you might need.

However, since you said it would be a deer stand gun, I think the .50 ML is the better choice.