A ready home lets you inspect the actual flat, see the neighbourhood at rush hour and move in within weeks. The trade-off is usually a higher price per square foot and less room to negotiate on payment terms.
An under-construction home is typically cheaper at booking and often comes with staged payments, but you may pay rent and EMI at the same time while you wait. Delays are the biggest risk, so treat the possession date as a range rather than a promise.
A useful rule of thumb: add the rent you will pay until possession to the price of the under-construction flat, then compare that total with the ready option. If the gap is small, the certainty of a ready home often wins.