Why would you choose one build over the other?
The key to Melee is using the right setup verse your opponent. Depending on what your opponent is using, you may need more AR, or more defense, or less AR; allowing you to have more damage, etc
What is the difference between the ar/defense/damage/life between each build?
I won't give exact numbers to reveal my characters stats.. but I can give some rough ideas of what to use when. I do plan on making some generic screenshots in the near future, since they seem to be at a high demand.
10frame fort-- Very high damage, High AR, Lower attack speed.

this is best to use verse other slow attacking concers
9frame fort--- High Damage, lower AR, Higher Attack speed

this is best to use against zealers using Levi or Fort, because their defense wont be too high and they hit frequent, so the fast attack speed will help. This would also work well against jabbers or furies
10frame Prudence -- Very high defense, High AR, decent damage

This is good against non angelic barbs.
9frame Prudence-- Very high defense, high AR, decent damage

This is good against non angelic zealers.
E uppd B hades-- Good defense, very high AR, decent damage

This build puts you in the 9th frame, and works best against zealers with prude or shaft, because they will have higher defense and you would need to use angelics to crack it. This also works well against barbs with high defense (prude or other bhades builds)
Steel Cara-- This build puts you in the 9th frame, and works best against zealers using levi or fort, because your AR will be lower but again attack speed up.
Gvalor-- This is one of the most rounded builds and I use it in almost all situations, but the AR may be too low to crack some Prudence builds.
Which build counters which build? You say the strategy is using the right build at the right time, list some examples.
^^ explained above
What's the difference between 9 frame and 10 frame attacks?
9 frame attacks are faster, you do 2.7 attacks per second. 10 frame 2.5 per second. Briefly explained above, in order to attain the 9th frame, you have to sacrifice damage, AR, or Defense, but sometimes its very necessary to be able to attack faster.