Henry makes a very high quality rifle for the money. Either will serve you well. The heavy barrel is cooler but it's heavier (duh), so if you have young shooters you may want to keep that in mind.

Be aware that the rifle has a very low comb and you'll find that a good cheek weld is nearly impossible. You can't really put your head down and go at it. Granted, many really good .22 shooters don't actually use the sights for much. My old man can look down the barrel and steer the bullet by the strength of his will.

10/22s are great, reliable rifles. But, they're semi-automatics. You have to clean them every now and then.