A non-condensing tankless water heater does the same job as a condensing one with a simpler machine. Water passes through a single copper heat exchanger over a burner, and the exhaust leaves at 300 to 450 degrees F carrying its residual heat with it. There is no secondary exchanger, no condensate, no neutralizer cartridge, no drain line, and no condensate safety switch to lock the unit out. Fewer components means fewer things to service and fewer things to fail.
The honest trade is efficiency and vent material. Non-condensing units land around 0.81 to 0.85 UEF against 0.93 to 0.96 for condensing. That is a real gap, but it is worth putting a number on rather than reacting to. A typical Frisco household needing about 165 therms of delivered hot water annually burns roughly 200 therms through a non-condensing unit versus about 174 through a condensing one. At North Texas gas prices, that difference lands in the range of 25 to 45 dollars a year.
Because exhaust stays hot, venting must be Category III stainless, typically AL29-4C or 304 stainless, which runs roughly $28 to $60 per installed foot against $6 to $14 for PVC. That single fact drives the entire decision. On a five foot garage sidewall termination the stainless costs almost nothing, and the non-condensing unit is clearly the better value. On a 40 foot run through an attic to a roof penetration, the vent material can cost more than the equipment savings, and condensing wins.
There is a third scenario where non-condensing is simply the practical answer: locations with no drain. Outdoor wall mounts on the side of a home in Newman Village, garage installs on a slab with no floor drain, or detached workshop applications all present the same problem for a condensing unit, which must dispose of roughly half a gallon of acidic liquid per hour. A non-condensing unit sidesteps the issue entirely because it never makes any.