So I've determined in the past that Champion isn't significantly weaker than Battle Master (and Eldritch Knight is fine also). Then Purple Dragon Knight comes along, and it seems rather underwhelming.
So the question is, compared to Champion and Battle Master, is the Purple Dragon Knight weak? I'd like to focus on the subclass itself, not worrying about whether its a good "warlord" or whether the fighter class itself is too strong or too weak, etc.
Kind of depends on what you mean by "weak."
They won't do the damage of a battle master or a champion.
What they'll do is contribute the damage of the barbarian or the wizard or the rogue getting a turn they usually wouldn't (from being healed or inspired).
So for the party, a BM gets superiority dice, a Champion crits twice as often, and a PDK adds +(barbarian damage). Or they heal when another character would, so maybe +(cleric damage).
That's
potentially a lot of damage, or other nasty effects. The trade off is that it's often harder to notice that "defensive contribution" - the goalie never gets the credit for success, right? It's also not always necessary. Healing the party back from the brink of death is useful, but maybe before the barbarian gets another turn, the battle ends anyway. When it matters, it tends to matter more, but it's often hard to see when it matters.
Of course, they also get their normal allotment of Fighter murderin' - Action Surge is just as much their bread n butter as it is for any fighter. Which is more than enough to fill the role of damage-dealing powerhouse, even without the extra crits or d8's. In 5e, not being the best doesn't mean you aren't good enough. They won't be the best. They're probably good enough.