It's relatively easy to play through as the Templars by occupying and releasing. You are spamming priests, aren't you? It's the easiest way to get unrest down, and you're going to want to do it anyway. On top of that you can start to generate unrest in Muslim held lands if you have enough of them. The only reason to sack is if you're going to get a decent amount from it, and I haven't always seen buildings get downgraded.
No reason to exterminate as I don't think the public order bonus lasts very long.
As to executing prisoners. I prefer to ransom them back. You can get several thousand florins, which can pay for necessary retraining/recruiting, and you deprive the enemy of funds. Several big battles in a row can bring in a reasonable amount. If they don't pay, well, you execute them anyway. The only reason to execute them is if you absolutely do not want them to be thrown back at you... if you captured a ton of prisoners in battle, odds are you kicked their butts, and you can easily do it again
The only time I executed prisoners was to prevent the survivors from returning to a settlement that I had just crushed, forcing me to lay siege once again.
I support the above with my Rise of the Temple Knights AAR, VH/VH on SS 6.2 (see below).