Pers'nally I wouldn't trade you my Lyman GPR for any 3 Thompson Centers.
If you go with the Lyman, you definately need to look into upgrading the triggers. The lock on the percussion model is basically fantastic & has pretty much no issues at all, but the triggers suck the big one.
However, for $40 or thereabouts, you can get a set of R E Davis, Deerslayer triggers & they're as good as any triggers on the planet.
The Lyman, as anyone will tell you, is capable of phenomenal accuracy (after a brief break-in period, usually 50-100 shots) far better than I've heard of with the T/C.
If you care about such things, it's also a dang sight closer to an original Hawken (at least, externally) than most 'modern' guns.
If it fits you (pretty important thing to think about) I think the Lyman beats the T/C hands down.
The Lyman has a lot more drop in the stock than does the T/C & that may be an important factor to you. Definately try them both & see which fits you better.