In my experience the paid apps really are, in general, better than the free ones on the iPad.
For instance, I love to paint and draw. You show me a free app or 2 similar in quality as say SketchBook Pro or ProCreate?
Ms office stuff, ie, excel and word - show me a freebe that, not only does what the equivalent paid versions do, but that work in the first place?
Still yet to find a free office organiser app that does the job.
This is not lack of research I assure you, and I'm only talking general apps here too.
And another thing you might like to consider, the paid apps are usually more polished and finished to a nicer look and feel, ergo making the user experience that little bit better even if they do the same as their free cousins, and there's so many peeps out there, me included, that think nothing of spending a buck or 2, and that's generally all it is, on apps.
Not everyone had the ipad as a gift, or is a kid, student or unemployed person that can't afford apps. Most of us bought the iPad out of their own means, and if you can afford that then you can afford the apps to go with them. It's like buying a Ferrari and complaining about the cost of the petrol.
I'd much prefer a paid app than it's free brother generally just for that reason alone.
There are those of course who stead fast refuse to buy apps when they can strive to find a free one, and if they can't they only complain at the cost of the paid ones. I've not got much time of day for this argument.