I currently own one of each (previous includes H-14, H-18, H-20)...

Given what you've said about sailing ability and the fact that your kids are teen-aged and you're looking to grow into, I'd say either is a viable choice.

Spin sailing a cat is addictive, so it's easy to give the nod to the N-20. But the 6.0 is still fast, simple, fairly bullet proof and you could always add the chute later. The 6.0 also sails pretty well without the jib, and some use a 5.8 jib to take some of the power out, so there's some easy options for toning it down a bit.

A biggee to consider IMO is your venue - will you store the boat rigged and ready to go, or will you trailer and rig each time? If the boat stays rigged go N-20, if you rig each time you'll get on the water much faster rigging the 6.0. Since you're rec sailing you'll probably be doing more blast reaching instead of windward/leeward, and again the 6.0 ain't bad there.

Don't make your first day in either boat one with wind over 10-12. Scale things appropriately for the kids, then go nuts. Your biggest problem may end being how to wipe the smiles off your faces...