I think the core focus of the subclass is to keep fighting, for that you don't have some extra limited resources as the other subclasses but I think those at low levels can keep fighting longer because they are doing more damage or using maneuvers/spells for survivality. The other subclasses also have an extra feature at lvl 3, the Champion only starts with some random extra damage, you need to roll a 19, that's very bad.
Later with remarkable athlete and second fighting style the Champion receives a good but subtle combat boost (and some other improvements beyond combat). More initiative means some encounters will end faster and less hits received, the second style gives them more versatility for different encounters or more survivality for them or companions. The improved criticals will get better as you lvl up beyond lvl 10, with an extra attack at lvl 11, superior critical at lvl 15, extra action surge at lvl 17, extra attack at lvl 20. Survivor is very good and not subtle.
My solution is to give the Champion an improvement for second wind as a second subclass feature at level 3, 10+CON instead of 1D10. This means 5-10HP more on average and second wind becomes a reliable source of extra HP. It will be more important at low levels, just what I want.
For example our dwarf champion had 34 HPs and could heal 17 using second wind, a nice upgrade for him, at least he felt he was a tank, before that the paladin of vengeance of the group was delivering more hits and criticals (luck and advantage/short rest), better saves, more damage using smites and had a reliable heal...