Taking a quick look at your Lodestone profile (assuming this is your best gear), you have 6446 HP. If the PLD had 7129 HP, there's actually quite a big gear difference there. Something a lot of people don't seem to know is that WAR and PLD both have two different tanking stances - Defiance (WAR) increases your base HP by 25% and increases healing received by 20% whereas Shield Oath (PLD) reduces damage by 20%. These, baseline, are equivalent to eachother. So the best way to tell who actually has more HP is if you have more than the PLD without Defiance on.

Now, specifically for Titan EX (imo) it's better that the PLD is off tank regardless as they have access to Hallowed Ground and Tempered Will which greatly reduces their worry about avoiding landslides during the add phase. A WAR is perfectly capable of doing this as well, its just slightly more complicated (Holmgang can also stop landslides from knocking you off, though it also stops you from moving).

There are fights where PLD is a better MT than WAR (mainly for Hallowed Ground), and there are situations where WAR is the better MT (fights with predictable bursts of big damage, IE death sentence in T5). Both tanks can tank equally well, as Moonwolf said, so when deciding who should MT and who should OT its usually on a fight to fight bases and based on who's the more geared of the two. I don't really agree with WAR always getting stuck on the OT role (as the combination of WAR MT/PLD OT actually does more damage than PLD MT/WAR OT when played properly) but if you get stuck with that job then you're just going to have to suck it up and queue a Butcher's Block.