My character at first went to the mages because Fiona seemed the more reasonable sort compared to the Lucius and was just focused on sealing the Breach, then I find out a magister pretty much enslaved them (Fiona being an idiot) and that he was responsible for messing with the fade rifts at Redcliff with time magic and could potentially mess up the world. I felt that was more important than reports on something wierd happening to the templars. I ended conscripting the mages, mainly because they were out of control due to weak leadership (Fiona) than any desire to pick a side.
On my second playthrough, I picked the templars because the mages seemed fine (I didn't go to Redcliff and find the time altering portals) while we were getting reports on something fishy about the templars. I ended up conscripting them because I felt there was no good people to lead them (Ser Barras died on me.).
This current playthrough for me, I am going just ally with the templars instead of conscript them because I'm going to ensure that Ser Barras survives this time. I'll do one playthrough where I ally with the mages but I don't think I'll ever be able to actually pick it again after that due to how weak the mage rebellion leadership is.
Templars easy, They are a well trained professional army far less likely to succumb to demonic posession, They are looked upon more favorably by the public so it will do wonders for your diplomacy to have them on side considering they are viewed as hero's (All your companions confirm this if you recruit them). If you're someone desireous of mage freedom you can still get them their freedom by siding with the Templars.
But most importantly in the epilogue the mages always leave you, you can convince the templars to stay by your side and make up the core of your army.
Actually, I think they lost some of that reputation with how they behaved in the war before DAI and in the game itself. Both sides are in the crapper as far as reputation goes in my opinion but it's up to the inquisition to salvage one side or the other.