The phosphor formulations in bulbs are not all that meaningful. The Halophosphate is just a type of mixture which is made up of a single type of phosphor and is combined with some other elements to generate the colors the manufacture is after. They just add stuff to the phosphor compound like Antimony or Manganese or other exotic compounds. Supposedly, the single phosphor with added ingredients makes it difficult to achieve color fidelity but it's less expensive. Halophosphate coated bulbs have been around a a long time. They are really the bog standard in a way.
The other type, the Triphosphor, combines different kinds of phosphor mixes using multiple layers such as red phosphor+green phosphor+blue phosphor. These different phosphors compounds have different native colors because of the weird molecules that phosphate (PO4) can be combined with such as rare earth metals (bizzaro metals like Cerium, Terbium, Lanthanum). Of course it's not like you can go to Tesco and buy some Terbium, so that's one reason these bulbs are more expensive.
If I'm not mistaken these types of bulbs were made popular by products like the Triton Bulbs. I believe they produce multiple energy peaks, or at least tailored energy distributions, to get better CRI. There may be other advantages like longer life or efficiency and so forth. But why do you care about CRI? And why would you want to pay megabucks for high CRI which has nothing to do with plant growth? Don't you like the colors of the bulbs you have now?