Cascade1911 - I would say that it depends on which one you like the best. If you are going to use it for reenacting, you are going to be limited to either the 3 band Enfield or the 3 band Springfield.
I have always liked the 1861 model. I used to shoot NSSA and I have used an original 1861 model as well as having the experience of shooting the 2 band Enfield, 3 band Enfield, Zouave and Mississippi Rifle. I used a friend's 3 band Enfield once in a long range shoot whre we shot targets up to 1000 meters. If you are just going to use it for a "shooter" - any of them are fun.
If I were to go back to shooting muskets, I would seriously look for a good 3 band Enfiield or a 2 band Enfield. I had an original Barnett Enfield and I enjoyed shooting that when I was a kid. I encourage you to handle and feel the two different models if you are considering them - there is a different feel to them. The only way that I can explain it is that to me, I feel that the Enfield has a little bit straighter buttstock and the forearm feels thinner than the Springfield model. The "comb" of the buttstock of the Enfield is lower and straighter. It really depends on what feels best to you.
The important thing when shooting the rifled musket is to get a minie that fis your bore well. You don't want a minie that is too much undeersize as it will "keyhole" when fired (tumble). You might be able to fire the minies just as they come from the mold or you might end up having to "size" them.
If you have had the opportunity to handle originals of the models that you are looking at, bear in mind that the repros will "feel" different. I have a 1855 repro that is basically the same as the 1861 with the exception of the Maynard Tape Primer door. It feels totally different than my original 1862 - the repro is heavier.
Both models are nice rifles and you may have other things that influence you as well such as what your Civil War ancestor may have used - as has been stated. Whichever one you choose, I think you will really enjoy shooting it as they are lots of fun. Good luck!