i have shot a .5", 4 shot group at 100 yards with my omega.
the poll is rather useless, because most people either buy the omega or the encore, and not both, and therefore don't have a lot of experience with the other.
i obviously bought an omega. never owned or shot an encore, but i'll say this. i previously shot a NEF huntsman. i ended up getting rid of it because as i shot it, fouling would cause lock-up problems - the breech needed to be slammed shut to ensure it locked up properly. of course, good cleanings took care of this problem, but nonetheless, it was a hassle i didn't need. furthermore, i experienced some blowback with the break open NEF, which doesn't really affect performance, but can dirty up a scope. i don't know if these problems are inherent to break actions or just NEFs, but i suspect that its the action type.
chuck hawks said that the encore is great shooting, not because of its action, but in spite of it. i tend to agree with him. the barrel accessory program is nice, but it too has its drawbacks. POI problems have been detailed in other forums, as well as other problems.
the omega is pure muzzleloader. simple to load, simple to clean. shoots extremely well.
the problem described with the breech falling during travel is unique. i've never heard of that before. mine has a distinct snap when you raise the breech. there's no way it would open unless i opened it.
encores are great guns. so are NEF's. i don't like the barrel accessory programs, because i feel i'd need to test fire every time i swapped a barrel. i'd rather just buy a new firearm. obviously, comparing prices, the NEF's make that more reasonable.
whichever way you go, i'd recommend making the gun a permanent muzzleloader. obviously, with the omega, you have no choice. but if i got an encore, i would use it strictly as a muzzleloader.