The key difference is size. There's a lot more meat in your typical prawn, and this allows you to peal and prep it in a way that distances you from its natural appearance. There's less meat inside the cricket, so you pretty much have to eat it whole, shell and all. The resulting texture is less meaty and more mealy/crunchy.
In my experience eating crickets, I've always been aware that I'm eating crickets. There is no fantastic way to mitigate the texture and the mouthfeel, shy of grinding up the crickets into a powder and reconstituting them in some other form.
(The texture doesn't bug me per se, but it sure does seem to bug a lot of people who've tried crickets. No pun intended.)