My goodness, so many guides out there on this exact topic. I Googled 'ffxiv paladin vs warrior' and came up with:
https://www.google.com/search?source....0.UiYIvbedeDw

I looked at many of these same guides when I was trying to decide which one to level up first. Went with PLD, but now working on my WAR. Also, there are lots of these same discussions on this board. Basically, Warriors are a little more challenging to play but can tank all content up to the hardest end game stuff just fine, though they sometimes give healers not used to them some heart palpitations as they see their HPs bounce around. While I am not in Coil yet, I understand that some of that content is more difficult for a Warrior, at least as main tank. To address the issue, SE plans some possibly significant buffs for the Warrior with Update 2.1 planned for sometime next month.