The choice hinges on which rifle style that you prefer the most.
The Traditions guns perform great, and their Kentucky rifle is very accurate. I have several of their models without any complaints.
But every model has features and drawbacks that require scrutinizing to be confident in one's decision.
I personally like rifles that are faster & easier to handle and load, and the full stock and longer barrel length of the Kentucky hinders that to an extent. It doesn't have a hooked breech for easier barrel take down and cleaning, and the longer barrels do collect a little more fouling in the breech which makes loading more difficult during routine shooting unless the shooter swabs more often. The patch lub doesn't always reach the breech, and ramming also requires a longer stroke, so easier loading is an issue.
The Kentucky's trigger, trigger guard and wrist area aren't as ergonomic, and the longer barrel is more unwieldy. The shorter length of pull, which helps hold the longer barrel could be a comfort issue for some.
While it does have more long range accuracy potential and is more forgiving to sighting errors, in reality an inch or two at 50 yards isn't a major factor considering the negatives.
Looking up the Trade rifle, it's 14 inch length of pull might be a plus for some, and it appears to have a more ergonomic wrist, trigger and trigger guard. The 28 inch barrel is about the maximum length for a faster handling rifle to have, and it's a Hawken type design with a single trigger. It appears to have a hooked breech barrel for easier take down and cleaning which is a plus. If the rifle isn't being lugged through the woods, then it should get the nod over the Deerstalker due to barrel length. Lastly, the 1 in 48" twist does have more versatility, and even the Pedersoli Kentucky has the 1 in 48" twist and shoots patched ball just fine.
If there's a rifle style that's preferred, then choose that model.
But if you're open to any of the models mentioned, then the Lyman Trade Rifle may ultimately be the better choice.