I don't speak from experience because I don't have one, nor will I ever because I have a family that just wouldn't fit. But I did go through a bit of obsession with them a while back.
Again, just me, but these aspects appealed:
1) aesthetics. You get the adorable country cottage look that is very expensive in a full sized home, but at a fraction of the price.
2) customizable. If you need an office space, you have one. If you need a sunny front room, you have one. You get to choose the whole layout based on your needs.
3) light. Every tiny home picture I've ever seen is about 100x brighter than an RV. (Again, aesthetics)
4) illusion of permanence. An RV is a vehicle. It will always be a vehicle. Many of the tiny homes, even if they are attached to trailers, have steps built on and are usually fixed to more permanent utility set ups. I would more easily be able to see myself living in one long term.
5) space. I don't know if this is true, but because of the typical set up with a loft bedroom space, the tiny homes seem much bigger in terms of useable space than an RV. Plus all the space, because it's customizable, is fully utilized and functional for your own needs.
Just my thoughts! I'd love a tiny home, but I actually need a normal sized home that is efficiently built. Small rooms are fine, but I need an open kitchen or open plan space for a living area. I need full sized heaters/water heaters for a family with multiple kids. They are super cool but definitely still have a lot of the inconveniences of RV living.