Math warning, it's easy.
Level 3 Champion
+5 to hit, 2d6*+3 damage, 19-20 crit; vs AC 13 (65% hit, 10% crit)
11.33*0.65, +8.33*0.1 = 7.3645+0.833=8.2 per attack
Level 3 Battlemaster
+5 to hit, 2d6*+3 damage, 20 crit; vs AC 13 (65% hit, 5% crit)
11.33*0.65, +8.33*0.05 = 7.36666...+0.4166... = 7.78 per attack, +13.5 per short rest, or roughly 40.5 per day.
Level 3 Eldritch Knight
+5 to hit, 2d6*+3 damage, 20 crit; vs AC 13 (65% hit, 5% crit)
11.33*0.65, +8.33*0.05 = 7.36666...+0.4166... = 7.78 per attack, plus 2 spells per long rest (
3 times per short rest, the Battlemaster has a standard action attack for an average of 15.83 (oh, and they don't waist it if they don't hit, because they don't use it unless they hit generally). That's nearly 3d10 damage, which is more damage than a 1st level single target spell deals. I know that a single target damage spell isn't the best use of an Eldritch Knight's spell slot, but I'm looking at equivalencies here. The Battlemaster gets 3/short rest of their ability, which amounts to about 9 a day with two short rests, while the Eldritch Knight gets their ability twice per day (though the new SCAG cantrips do make them cooler).
The Battlemaster has too many dice at level 3. The Champion needs to drop slightly more than 10 attacks to equalize their damage with a Battlemaster having 1 die; even that's a lot to ask for with the way things are balanced now. At about 3 rounds per combat, with an action surge, the Champion will get like 7 attacks. If crits included all damage, it would get slightly better, but not by much.
That's why the Champion looks bad. The Champion doesn't look bad compared to the EK. They just look bad compared to the BM.
Also, someone was comparing the Battlemaster to the Warlock. The Warlock is a full caster, akin to the Sorcerer and Wizard. The Battlemaster is akin to the Eldritch Knight, who has a slower spell progression than the Sorcerer, and slower than the Paladin. So the Warlock having more spell slots then the Battlemaster has maneuver slots per short rest will never bother me; the Warlock has more spell slots than the EK over the course of a day too.