Having shot both competitively , I definitely prefer the Springfield simply because the stock fits better for me for off hand shooting and so I prefer it .The same stock dimensions are on the 1861 Colt Special model as the Springfield . The Enfield was an English made Parker Hale 3 band . The Springfields were parts guns made up of original parts , new Whitacre barrels and pre-carved stocks from Dunlap. While not originals, all are quite representative dimensionally and as a bonus shot minies very very well .
The sight on the Enfield is better from a shooters point of view .Enfields are actually shot with the shooter more squared to the target as English period photos have shown (sorry I can't recall which book I saw the photos in ).Does this matter to reenactors ? No idea . Most seem to be aiming their volleys high in live demos I've watched ,for safety reasons and not so worried about style points .
Cleaning was never an issue for me for either but I can see why a reenactor would prefer a more rust resistant blued barrel in the field . If you end up with a '61 Springfield grease the clean out screw on the bolster occasionally otherwise they are the devil to get out . If you're buying a used one make sure it can be unscrewed. Use it during a major cleaning and it will help prevent misfires. I never had an issue with the turn screws on the barrel bands on either the Enfield or the '63 springfield .Yeah it's a little slower to take down then a '61 but it depends if your just field cleaning or taking it apart for a serious bench cleaning after weekend of shooting .
Since you're not actively shooting it with live rounds ,I guess I'd be open to either depending on what kind of deal I could get on a used- but- not- abused repro rifle musket and what is recommended by the group you're working with.