Here's what I have now - thanks to everyone who made useful and constructive input.
So here's what I have now:
Second Wind
You have a limited well of stamina that you can draw on to protect yourself from harm. On Your Turn, you can use a Bonus Action to regain hit points equal to 1d10 + your fighter level.
Once you use this feature 3 times you must finish a Long Rest before you can use it again.
Action Surge
Starting at 2nd level, you can push yourself beyond your normal limits for a moment. On Your Turn, you can take one additional action on top of your regular action and a possible Bonus Action.
Once you use this feature 3 times you must finish a Long Rest before you can use it again.
At 17th level you may use this feature an additional 3 times before finishing a Long Rest.
Ability Score Improvement
When you reach 4th level, and again at 6th, 8th, 12th, 14th, 16th, and 19th level, you can increase one ability score of your choice by 2, or you can increase two Ability Scores of your choice by 1. As normal, you can’t increase an ability score above 20 using this feature.
Action Hero: The Level 8, 12, and 14 Ability Score improvements may each be replaced by one additional use of Action Surge per Long Rest.
Unlimited Might: The level 16 & 19 Ability Score improvements may raise an Attribute above 20, but not above 24.
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I think that puts the Champion Fighter on par with the Barbarian. They remain less durable but have very strong striking power for a limited duration.
So here's what I have now:
Second Wind
You have a limited well of stamina that you can draw on to protect yourself from harm. On Your Turn, you can use a Bonus Action to regain hit points equal to 1d10 + your fighter level.
Once you use this feature 3 times you must finish a Long Rest before you can use it again.
Action Surge
Starting at 2nd level, you can push yourself beyond your normal limits for a moment. On Your Turn, you can take one additional action on top of your regular action and a possible Bonus Action.
Once you use this feature 3 times you must finish a Long Rest before you can use it again.
At 17th level you may use this feature an additional 3 times before finishing a Long Rest.
Ability Score Improvement
When you reach 4th level, and again at 6th, 8th, 12th, 14th, 16th, and 19th level, you can increase one ability score of your choice by 2, or you can increase two Ability Scores of your choice by 1. As normal, you can’t increase an ability score above 20 using this feature.
Action Hero: The Level 8, 12, and 14 Ability Score improvements may each be replaced by one additional use of Action Surge per Long Rest.
Unlimited Might: The level 16 & 19 Ability Score improvements may raise an Attribute above 20, but not above 24.
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I think that puts the Champion Fighter on par with the Barbarian. They remain less durable but have very strong striking power for a limited duration.