A couple more points to consider based upon literature I have read:

Ringed engines are typically more expensive than non-ringed.
Ringed engines take longer to break-in (as Geistware mentioned).
Ringed engines will last longer before requiring service due to compression problems, and compression problems are much less expensive to repair - just replace the ring.
Ringed engines are less efficient (use more fuel for less power), due to blow-by past the rings.