Well the Lyman is more true to the classic "Hawken" rifle styling than the TC. The TC is going to be styled in more of a generic "Trade rifle" fashion IMO.
If your a purist the coil spring on the Lyman will drive you nuts but the lock functions well.
Both will benefit from a little "fluff & buff" of the lockwork. Pay mind to frizzen hardness.
If your of the mind superior aftermarket locks are available for both.
I feel the build quality is better on the Lyman and as mentioned, is more historically accurate. I've never owned a TC, they never appealed to me in the least.
One thing that needs improvement on the Lyman is the beavertail cheekpiece. IMO it is waaaaay too big, in factory form it just looks like a big fugly wart on the left side of the stock, especially the lower section. Reducing it results in a much cleaner look, more accurate to original "Plains" style examples I have seen.
Original rifles were examples of efficiency and function, if it didn't belong it wasn't on it, especially in the stock. Just enough to do what it needed without sacrificing strength.