Flip a coin.
More reasonably, think about how you want to deal with batteries: C (large, cheap, longer runtime, readily available) vs 123 (small, relatively expensive and hard to get, shorter runtime, but has benefits of lithium chemistry).
I have a Hyper-Lux V and an original model Tri-Star 3x3 modded to run on 4 C batteries, which should be roughly comparable to the Tri-Star Phazer. Here are some thoughts:
Yes, the Tri-Star definitely puts out more photons, but it doesn't seem twice as bright.
Build quality of TS is good; build quality of HLV is great.
HLV is pocketable (in a coat pocket or cargo pocket); TS isn't.
TS should have longer runtime, though I forget what they're each rated for. I haven't tested runtime myself.
TS has a bright white beam with bluish tinge; HLV has a creamy white beam.
TS has a larger and brighter hotspot.
HLV has a much better corona. It's smaller than the spill light from the TS, but it's brighter and therefore more useful.
TS throws better than the HLV, but not hugely so.