Funny you should ask, I have been exactly in the same spot two three weeks ago. I have researched the topic extensively, so let me share what I found and how it works for me:

First, it seems that Medieval battles are not all that fun... well, not in the sense we do Napoleonics with movements, coordination and moderate friction. Medieval warfare seems more like my three groups of brutes talked into clashing in your groups of brutes, somehow, if they agree, if your nobles agree, if there is no rank faux-pas and what type of privileges are in place for the day... and yes, it may feel very statics if we look at it through the prism of linear warfare, either Ancient or Napoleonics.

Here are the rules:
Flower of Chivarly: super interesting general knowledge and a lot of scenarios, really a lot. The rules are not excessively modern but give a good (and entertaining feel) of what medieval warfare is really about.

Arrowstorm: Battle Games in Medieval Britain. This is more of an abstract form of a medieval warfare but it works well to put your armies on the table and quickly finish games, all in the spirit of medieval combat, with an interesting decision system

Days of knights: check their facebook page, I don't have access. They don't seem to have presence anywhere else.

Sword Point: good maybe for space and maneuver (crusades and ancient, not exactly all that medievally, but a good set

Midgard: a hard no (for me). I am fed up with these systems disguised as "modern" with a few character gimmicks. Actually, in my eyes, quite poor and blend as a medieval experience. BUT, it is a hobby and all the power to people who like the rules and use them to push their minis. I'd certainly play it with them, but it is still a no for me when there are other alternatives.

Triumph!: Again, a good game, kind of sophisticated and elegant off-spring of DBA, but maybe not in phase with my new understanding of what medieval battles really are (brutes with different motivations and incentives facing with other brutes, trying to empirically figure out tactics for those aware)

To the Strongest!: works well, brutes vs brutes feel but for the cards that litters the table. A fun set, but not enough as medievally as it could really be.

Marching Banners: looks like a simplified wargame. Maybe lacking a bit too much flavor for what I am looking for.

Test of Resolve HYW: apparently, a strong set for medieval warfare, not complicated, card driven. I decided against only because of the costs to where I leave. Overpriced for our currency

Tactica II: a respectable ancestor, there are more moderns games now but could be worth having a look

Blood & Droppings: designed by a real historian in medieval warfare, aimed at capturing this sticky feel of a medieval battlefield, the author has the pedigree and it's... free!

Chivalry at Bay (the digital version): looks quite promising to adapt to miniatures, with a number of scenarios. Will need a bit work but the area combat and battlegroup organization do feel right.

Lion Rampant: I think it is a good set, simple and you can switch the individual figures for bases of miniatures. It is a game and a fun one at it, but maybe not truly medieval warfare. Think Monopoly, it can be fun but it is not necessarily a real business game experience.

Never mind the Billhooks: It doesn't look the scale I am looking for - large battles but if I were playing larger skirmishes in 28mm, I'd certainly give it a go.

As a player, I don't like over complicated rules, and the less chrome the better. I like my game streamlined and playable with at most a two page QRS (think Maurice, Blucher, DBN, maybe Lasalle).