Why should you build tank Jax instead of hybrid Jax? The first and main reason is cdr. Most people know that cdr is overpowered on bruisers but they don't really understand why. With this build at lvl 18 you have 32.1% cdr, which means that the cd on empower is exactly 2.037 seconds. Since Jax has one of the highest base damages at lv 18 of 117.05, procing trinity force as often as possible will give the most dps possible. Also the cd on leap strike will be just over 4 seconds allowing you to stay on your target much better. Second, since Jax's abilities scale awfully with ad and even ap to an extent, building damage is very inefficient. Since trinity force only scales off base damage there is no reason to get bonus damage. Lastly, defense is better than sustain because you won't be focused down early in a fight allowing you to jump the carry and kill him.

A little extra. Cdr is exponential meaning that every additional percent is better than the last one. This is why building a lot of cdr is so good. Below shows how much more often you can use abilities with the corresponding cdr.
10% = 1.11
20% = 1.25
30% = 1.43
40% = 1.67
32.1% = 1.47
So 40% cdr equals an increase in abilty dps of 67%. Ignoring the increased trinity force procs, Jax would need 142 ap just for the dps on empower to equal empower with 32.1% cdr. When you combine ap, cdr, and trinity force procs, you will be doing more damage than if you build only ad or ap and you will be able to tank so very hard. Plus aoe stun so good for initiating.