The skerry is lighter.  I cartopped mine the first couple years, but have it on one of the Trailex trailers now and am glad.  I had engineered a way to get it on and off solo, but it was still a bit much.  The NE is definitely heavier.

If I were taking more than one crew, the NE is the better probably.  The skerry has you sitting in the bottom when sailing and it really wants someone between the middle seat and the mast with another aft the middle seat.  The skerry is a very easy rower if thats your thing.  Add an additional rowing station so you can move around to balance the load.

If you have the resources, I think the Southwest Dory would be a great family boat.  The side tank seats would be better for sailing and much more space and bouyancy.  Ive looked at it and it is a definite step up in build complexity though.

   And on setup, depending on the rig, they should be about the same.  Especially if you get the lug rig for either, get it with a reef.  That may be standard now.  If I were getting the gunter sloop rig, I definitely would get a reef set up for the main.  The skerry is a very easily driven displacement hull and you need to reduce sail in a breeze to keep control downwind.  I bet the NE is similar.  The sloop will be more rigging time, since it has the shrouds and stay, but still shouldn't be bad.  The lug is dead simple to rig.  It's about as easy as a Sunfish to rig.  The sloop should balance better than the lug downwind.  

   Kids get bigger in a hurry.  And if you are to do any excursions at all, extra space for gear will be greatly appreciated.  The lug rig (on either boat) will sail just fine and will rig very quickly, and store more easily in the boat when/if the rig is down.  Reef points were standard on my sail as of 2 years ago.  I did build a bigger rudder blade for my NE Dory to improve both very low speed stearage, and also stearage when overpowered.  Plenty of room for tandem rowing on the NE Dory, less worries with oar sychronization (but synchromization is still necessary, just more room for error).  Look in the forum for ideas on NE Dory "side seats" - in my opinion they make sailing much more comfortable and don't really occupy much space that was otherwise very usable - you can even add floatation under them if desired - I think the side seats and floatation are both good idea.  Both boats (even with the added floatation) are nearly impossible to self-recover (get bailed out) if capsized in open water with decent waves larger than 8-12 inches, just take this factor into consideration for safety concerns. Length and weight will make a Skerry easier to cartop.   You probably won't want to cartop the dory (unless you have a strong 14 yr. old for help?).  Maybe if your pop up camper is strong, supports (2x2's ?) could be laid across the top of it with the boat carried there, but trailering a NE Dory independently will certainly be easiest - the trailered boat provides a place to carry o whole lot of stuff - sails, rudder, daggerboard, oars, anchor, life jackets, etc., etc..and will provide a place to store the boat (and many of the same items, if under a good cover) when at home.

Don't neglect to take a look at the Jimmy Skiff II. The NE Dory is "prettier" to my eye, but given your proposed usage, it provides another option (one that includes a motor), but of course you get to decide what is best for you.  

Thems my thoughts.  Good luck and have fun with whatever you do. 

  And another thought - suggestion:  You mention a sailing club.  Anywhere that large numbers of boats are stored, there is usually a pile of junk boats and trailers - people just move on and "donate" or abandon them.  Finding a small boat trailer that can be set up to take any of the CLC designs might be done for little or no money if you find one of these piles.  You might have a like-new trailer for the price of bearings, tires, paint and lights. 

   I have a Skerry.  I didn't build the NE Dory because the boom appears a bit too low.  Every time you tack or gybe, it looks to me like you better get out of the way.  Not so w/the Skerry boom.  Boom's high enough that you don't have to move your head when tacking.  And when rowing, if you sit on the middle thwart, you can easily reef up that end of the boom so as to be up above your head.  That way you can revert to rowing in the Skerry, without having to lower the sail.  Good luck on whichever boat you choose.