I was planning on a continuous flow when my 19 year old service goes, but read they need a minimum flow rate to kick on. Our area seems to get about 22 years to a service. Serendipitously we recently spent a weekend at a home with a continuous flow service and found it challenging. I suspect there is a learning curve to using them as you cannot have arbitrarily slow flow hot water, but that could be model dependent. Most I looked at also required larger gas supply lines than storage systems, so scope and allow for extra installation costs if you need anything upgraded.
Since continuous flow systems only fire up when you use hot water, and have high efficiency heat exchangers, they have higher energy star ratings than storage tank systems. What that means in a gas bill, no idea Any operating savings need to be balanced against total installation costs amortised over the expected lifetime.
Addenda - the Rinai 26 Continuous Flow model spec states "Compatible with low flow rated shower fixtures (3 Star - 7.0 to 9.0 l/min)" but my shower head max flow is 6.5 l/min, if that reinforces the flow rate problem vs your needs.