I'm going to speak as someone with extensive Traditions experience, since those are the only muzzleloaders I've ever owned.
I started with a Deerhunter. Solid beginner gun for $120. I could hang the gun from my finger by the trigger without firing it though; had a gunsmith friend go to work on the sear and it pulled GREAT. Killed several dozen deer with that gun at up to 198 yards; open sight groups at 100 yards averaged around 2-3". After about 6 years it mysteriously began shooting further and further to the right, and after pounding the sights over again and again I decided it was no longer trustworthy. Never figured it out though.
Upgraded (sort of) to a Lightning LD. This was before the Omega/Encore days, and I'm a poor grad student so it was at the limit of my price range. I experienced the same firing upon bolt closing Randy desribed....but only after I tried to adjust the trigger to target poundage. Then it would fire if the bolt was closed without first engaging the safety. I inched it back up until it was safe and no more problem, but more pull than I would like.
The cocking gets hard after 20-30 shots from the blowback, and it is a PAIN to clean. Accuracy for the first 50-60 shots was not good, but after some breaking in I now outshoot some T/C guns. I can get sub-MOA with many lighter loads (up to 100gr). I free-floated the barrel with a Dremel and got 100+ loads to come down from 6-8 inches to 3-4 inches. Not bad for the price.
I'm not fooling myself though. It filled my needs at the time but when finances are better I'm getting a thumbhole Omega (unless something better comes out). I wouldn't recommend anyone buy a Traditions gun with the other choices out there.