In FFXIV BLM is based around pure damage and AOE attacks, constantly managing mana, with the downside being not able to move during just about all attacks. BRD is based all around setting up and managing DOTs and buffs, single-target attacks, and has the ability to run around while attacking. They play significantly different, and if you played a BRD as a BLM with TP instead of MP, you would be a horrible player.
I'm not seeing it, there is no "mana management" in FFXIV (Except some rare situations like T4) You just do your rotation that gets your MP back automatically, there is no /rest mechanic and such. TP basically got turned into MP, you no longer build TP, you have a stack of TP to use, that's why I said TP are essentially MP for melee jobs.
AOE power and dots (Both have them, anyway) are largely irrelevant when fights are about repeating your rotation and playing the Simon-says game and every class needs to be viable ever. You press 1-2-3 and stack INT gears with one job and press 3-2-1 and stack DEX gears with another one. Elements don't matter, enemies don't have resistances, CC don't matter. The game is designed so you can hop in and play any boss with any class so they to be homogenized as possible.
If you want to compare BLM and RNG in FFXI, they were both damage dealers, but their mechanics were different and they operated under different rules. RNG had to take care of accuracy and distance but their damage was physical, which lead to them being able to SC and everything. BLM worked with magic damage calculation and they could use the most common mage's tools (They could heal, sleep, gravity mobs, etc) and they could MB but never SC.
In FFXIV I never once felt like I was a mage because there was little difference between me and the other DPS playing the rotation game.