Good question, so I will try an answer.
The traditional muzzle loader, made for centuries, was the side lock, first in a matchlock, then a wheellock, then a flintlock, then a percussion lock. Today only the latter two are commonly made or reproduced for hunting and sport. Folks who like tradition will use one or the other. Those re-enacting historical events will, of course, use the type of arm appropriate to the original event.
Many states have special hunting seasons restricted to muzzle loading arms and participating can extend hunting time beyond the regular season. In some states, only traditional muzzle loaders can be used (PA limits their muzzle loader season to traditional flintlocks). In other states, the restriction is only to muzzle loaders, regardless of age or type.
For those states, arms makers have come up with muzzle loaders that are modifications of modern rifles of break open type or bolt action. These are made and intended only for hunting in muzzle loading seasons. While obviously, they can be used for target shooting the same as any other firearm, they usually are ruled out of competitions and activities involving historical type firearms.
The pros and cons depend on what the muzzle loader will be used for. If for hunting where both the modern and traditional are allowed, it will be a matter of personal preference. Modern types usually have better triggers and better feeling stocks. Some are easier to use than the traditional type, but not significantly so. As in most cases of "which gun", the answer is that, where there is no law or rule involved, it is a matter of personal preference.
HTH
Jim