I've had both and finally settled on an 11 foot Boston Whaler tender
as my only dinghy. But, I have a 42 foot boat and it wouldn't have worked as well on my last sailboat, a 32 footer (I had an inflatable for that boat).
I'm still young enough (55) to easily haul mine up and store it inverted on my foredeck. When, I'm 75, I admit that may not seem like as good a plan.
Hard shell (and speaking mainly of the Boston Whaler, that I have).
1. Almost indestructible
2. Can be rowed (miles in fact if you are in good shape)
3. Cost (cheaper to obtain, last forever)
4. Tows much easier, (when using the right set up)
5. Unsinkable (you could machine gun it, and it would still float).
6. Motors unbelievably fast with a large motor (mine will do over 30 knots with a 25 HP on it).
7. Sunlight has no effect on it.
1. Can't be deflated, it is what it is, all the time
2. Bumps against hull
, without a really good rubrail (like a thick Taylor Made).
3. Good ones can be heavy (my Whaler weighs 280 pounds)
4. Needs sturdier davits, is heavier to raise and put on the foredeck.
5. Is not going to plane with a small HP motor (important to some people, not important to others. I always hated other people zooming by me fast, so I really avoid doing it to others.)
1. Lighter (making it almost a necessity for older or less physically fit people)
2. Can be deflated and stored like that.
3. Motors well and easy to get on plane, with smaller HP than most hard shells.
1. Can be damaged, quite easily and unexpectedly, at times (I've lost
count of how many people I saw patching inflatables on my last cruise
, including me).
2. Can't be rowed very well (your motor quits and you are screwed)
3. Are much more expensive new, and it is hard to tell the real condition of a used one.
4. Only tows well in calm seas (tendency to flip over in really rough or breaking seas).
5. Can sink if tubes get punctured.
6. Some materials really don't like sunlight and should be covered when possible.
I understand why lots of people pick inflatables. They do have a lot of good qualities. You couldn't give me one, though.