Eugeny Davidov wrote:
http://www.youtube.com/watch?v=aTA9-lYs41A - cavalry against footmen in 20th century )

Supposedly a 1958 flick of engagement from eastern front in WWI?
Anyway: there were cavalry armies as long as Polish-Soviet war of 1919-21

Anyway whenever discussing cavalry vs infantry not only it is a question of "when" but a question of where, to be specific if we are talking about Eastern/Central European Plain or elsewhere, with more rough or "bocage" style terrain that severely impedes tactical/strategical use of cavalry.

Another factor: the availability of easy-to-use grain. Plains were always breadbasket for Europe. This translates for less costly grain and substantial income source - which allowed for fielding costlier cavalry. Loss of export capabilities for grain in late XVII century was important factor in decline of Polish Military, eventually leading to partitions etc. etc..

Life on plain itself lead to everyday use of horse as viable method of travelling in open country - so more people accustomed to saddle in first place.

Open plain also means less cover - so there was early adoption of field earthworks and Wagenburgs/Laagers/Tabors as both means of defence from harassing cavalry and platform for field artillery.

For early XV century there is also weapon disparity, with type XIIa/XVI/ XVII blades prevailing and shorter/pointy types (XV/XVIII) absent from record (according to Marian Glosek "Miecze środkowoeuopejskie z X–XV wieku"). Also there is Grunwald battle that is much different with both scope and usage of horse armies from any western-context battle of that period.

With that in mind - head-to-head pitched battle performance could be of less importance than overall strategic advantage in plains context that speed and range of cavalry gave - that was only diminished by widespread use of mechanized infantry/armour in WWII.