I'm probably late to jump in on this, but I'll throw in my $.02 since I just bot a Handi in 22 mag and I own 2 Contender's and a Pro Hunter.
The Handi cost me $130 out the door with tax. The trigger is heavy and needs work. It's going to cost $100 give or take to get another barrel (22lR) and ask NEF to do a factory trigger job on this frame. However, the gun is accurate and I am not sorry that I bot it. The barrel swaps on Handi's are not anywhere the ease of the Thompson Centers. With the T\C's you buy a barrel, put it on the frame and shoot it. None of this fit it up stuff.
The Contender frame's that I own cost me $250 each. I stoned and polished the trigger\sear myself and the pull's are 3.5lbs. The rifle stock cost $160 and each barrel cost average $225. So that's $635 for "one" rifle. However, each "rifle" after that cost $225 (average). I'm not including scope cost in either the Handi or the T\C. And, once I have the trigger "fixed" on the T\C, it's fixed on all future T\C's. For Encores I think the average cost could be $260 per "new gun" (pro hunter).
So, for another $125--Contender to $160---Pro Hunter, per "new gun" over the cost of a Handi, what you get is a Thompson Center.
Now, I don't know what "better" really means, because both guns will match (from what I understand) in accuracy in all calibers. However, I do like the 3.5 lb trigger pull that is consistent in all calibers on my Thompsons. The Handi, you either have to send in to the factory and do these 6 week turn around things, or buy 'em second hand. And second hand buys are just not as easy as it seems. If you not inclined to do your own trigger work, then you may want to factor in the cost of trigger work into each Handi that you buy if you don't do the X-tra barrel program.
So, I don't think there is an argument that one gun is more accurate than the other. But I do think there is the factor of convience of changing calibers while maintaining the same frame and trigger pull, and stock that the T\C's provide that the Handi's don't.
All that being said, I'm not sell'in my Handi 22 mag 'cause I like it too much. But I've kicked around a 22LR barrel for the Handi and the more I think about it, I may just get a 22 LR for the T\C. Only because I can just buy it, put it on and go shoot.
Dave