Doc - A few corrections. Tritium, like all moderately decaying isotopes, will continue to emit particles for many halflifes. It doesn't stop at 4. At around 6 halflifes, for example, it is still emitting at about 1.5% of the rate when the sample was created. The particle emitted is a Beta particle (essentially an electron). The Tritium is transformed to Helium after the emission.
The quality and thickness of the phosphor does make a difference. Also the actual amount of Tritium at the start can affect how long a night sight is useful. IOW, if there is X amount in sight A and only X/2 in sight B, then sight B will die out much sooner as far as visibility is concerned. The lesser amount can be due to the manufacturer including a smaller amount or the sights (or Tritium supply) might have sat on the shelf for a few years before they were installed. The effect is the same.