I don't see why any of that would have to change. You sell your home at the same time you buy the new one, and what you get from the sell goes towards the cost of the new home.
Money-wise, you're no longer throwing it away on rent, but paying down a mortgage that eventually is paid off entirely.
On top of that, you're also no longer racing against the end of the rent contract, and can wait a bit - or move earlier - to find a new place you really like.
The turning point for me was, here in Chicago, when I was renting and my dad sent me some properties with the costs laid out: These places were significantly nicer, and the mortgage cost per month was ~60% what I was paying in rent.