There are some threads on this forum that cover the pros and cons, but in short;
The goal is to provide sufficient light to grow what you have. It is measured in a value called PAR. Generally, the more the better up to a point.
All lights mentioned can grow corals. Hard corals and clams need more, soft corals and obviously fish only tanks need less.
IMO
T5's
Pros
Inexpensive
Relatively low heat projected into water
Grows most corals
Cons
Bulbs need replacement AT LEAST once a year
They don't seem to project very deep, so in deep tanks they don't work as well
Use high voltage, so some shock hazard
Poor ripple effect
Cannot be dimmed
MH
Pros
Inexpensive
Grows all corals
Penetrates deep
Makes nice ripple effect
Cons
Really heats up the water. Chiller is almost always needed when generating enough light to grow hard corals.
Bulbs need replacement 1 per year.
A bit more dangerous as they get really hot and they have associated transformers that can catch fire.
use high voltage so some shock hazard
Cannot be dimmed
LED
Pros
No heat projected into water
Grows all corals
Easier to hang
Safer as the emitters run on low DC voltage
They can be touched while running without burning yourself
Can be hung right over the water
Last 50,000 hours.
Makes nice ripple effect
can be computer controlled and dimmed
Cons
More expensive
Can burn corals if not used conservatively
In summary, it is important to note how much actual output (PAR) the fixture produces and over what area and at what depth.
LEDs are getting cheaper every day and I believe they will replace both T5 and MH fixtures in the near future. I would never use anything else other than LEDs again.
JIMO, please add comments as needed.