The Sentinel feat doesn't give you Advantage.
The Sentinel feat doesn't give you a stat bump.
The Sentinel feat doesn't increase your critical hit range.
True, the Sentinel feat gives other useful, unique and powerful abilities. Hamstring on AoO is no joke, and work super good with Polearm Master. But even that is besides the point because I only made the comparison too Sentinel too point out that getting an attack on reaction really isn't as unique as the person I replied to made it out to me. Heck, the afore-mentioned Polearm Master also gets it, and on a much easier trigger.
And ill mention it for the 3rd time. The stat bump shouldn't be there in my opinion either. It was a free addition from my DM's part (probably because he recently got Xanathar's, and almost all feats there have random +1's)
Here are 2 balanced feats:
Feat 1:
While wielding a finesse weapon in one hand and having a second hand free, your weapon attacks with that weapon score a critical hit on a roll of 19 or 20.
Feat 2:
While wielding a finesse weapon, when a creature misses you with an attack you may use your reaction to make an attack with that weapon against that creature.
...
If you must add power you could do this:
While wielding a finesse weapon in one hand and having a second hand free, your weapon attacks with that weapon score a critical hit on a roll of 19 or 20. Also, if a creature misses you with a melee weapon attack, your next melee weapon attack against that creature has Advantage as long as you make the attack before the end of your next turn.
These are fair suggestions, and If they saw print I would be more then happy with them, but I would like to point out that this feat wasn't really made with "fair" in mind, but with Great Weaponmaster (+polearm master) and Sharpshooter (+crossbow expert) in mind

I understand that they are not populair with some people, but they still exist and put a big disparity between 2-handed\ ranged martial classes and 1-handed classes\ build. One of the goals was to make a feat that atleast gives those classes a viable option if they want to feel like they are still putting out some competative numbers for a more combat-heavy campaign.
The way I see it the +crit range on the duelist feat competes with the reckless attack option from GWM\ SS, while the reaction-attack is quite comparable to GWM's bonus attack on crit\ kill. Ignoring cover for SS is harder to gauge, but I still would never want to be without it on an archer.
I can dig the finesse-classifications but I'm wondering why you feel dual-wielders should be excluded from this feat though, is it a thematic thing? Cuz Drizzt would take this feat. Is it a power level thing? Because if there are dual-wield builds that do anything close to ranged or 2-handers I'm all ears

I would also really like this build to work for any build that wants to use Booming Blade, or similar effects\ spells, with focus in off-hand.
Wether sword + board characters should be able to use this is a fair discussion, but I'm leaning to yes. It would make for a very interesting feat option next to Shield Master, with the prone on bonus attack giving advantage which synergizes with the +crit range (and once you specialize with 2 feats I think it's super thematic that your shield bash-attack combo becomes more deadly).
I think if you change the language of the crit feature so that it stacks with Champion, it works fine without stepping on their toes. I'm 100% ok with feats giving things that you can also get by multiclassing, as long as they can also be used to beef up that thing for that class, like Martial Adapt and Magical Adept.
The Repost, I'd say 1/SR when an enemy misses works. It no more steals the BM's thunder than Shield Master does, but what I don't like is that it gets kinda weird when you make a BM with the feat. I don't have any better solution than yours, though.
Also, damn it is pretty much the same as the Sentinel feat attack.
Yeah, I agree, I'm not sure how the wording would be on that though, "Increases your critical hit range by 1 when using a one-handed melee weapon" sounds kinda clunky. I think the riposte could very well be without advantage, but my DM argued that it really fits the man-to-man aspect of the feat, where you can capitilize on a single slip-up, and that even with the advantage the raw damage output of the feat still doesn't come close to a build that can use GWM\ SS 3-5x in a round.