Condensing boilers and water heaters save fuel by recovering the byproducts of combustion normally sent up the flue at 350°F or more. By condensing the flue gas in the heat exchanger, the heat is transferred to the water going to the radiation.
Low return water temperatures, typical in properly designed hydronic systems, and more easily in radiant slabs, are nearly always below the 'magic' 130°F mark where the appliance will hit 96% thermal efficiency.
Outdoor reset (ODR) insures that the supply temperature is never higher than what is necessary to maintain the inside design temperature. In my own garage the design temperature is 88° in the office and the low operating temperature in the main shop 52°F to maintain 50°F indoor temperature on the coldest days.
The Takagi, and all flame modulating burners, rely on supply and return sensors modulating and operating on both to insure minimum flow vs. output rates and in the case of tank-less water heaters a minimum return temperature. This is why we can't use tank-less on snow melting systems - even if we wanted to.
With condensing boilers, the flame will modulate to maintain design temperatures based on supply temperature and outdoor temperature inversely. The colder it gets outside, the warmer the water going to the slab. Higher efficiency and longer component life is the result.
With a tank-less water heater the flame modulates to maintain a fixed supply temperature, say 120°F. If this happens to be the design temperature for your particular radiant floor, you are all set, provided you don't mind operating the system year-round at a temperature only needed the few coldest days of the season. This by the way is how most residential boilers, water heaters and furnaces still operate today.
Properly piped, controlled and designed, a tank-less is an inexpensive way to drive a radiant slab, but less than ideal. We design many systems for folks upgrading to condensing boilers.
If you have to burn propane, condensing technology is the answer but each unit (especially on propane) should be tuned with a combustion analyser and regular maintenance never neglected.
In some areas off-peak electricity is a better option.