If you are currently running clinchers with rubber (butyl) tubes then you stand to make the biggest gains from switching to Nano tubes. You will save up to 300 grams of weight (2 tubes and 1 spare) for a road / tri / BMX set up and up to 500 grams for gravel and MTB. Most of that weight is rotating weight, which has a major impact on acceleration and handling. You will have lower rolling resistance and better puncture protection. You are effectively getting all the performance benefits of tubeless, without the downsides.

If you are riding latex you will see around a 150-200 gram reduction in weight, similar rolling resistance but huge increase in air retention and puncture resistance, plus Nano tubes are much more robust than latex when handling and fitting.

If you are running tubeless and sick of the hassle of maintenance then TPU tubes offer you a great option without any real loss in performance. If you are happy running tubeless that's great, but you always need a spare and nano tubes take up almost no room in your spares bag.