I have troubles to understand the differences between TileStache and Geoserver.
My goal is to serve tiled geoJson through a restFull API and consume it with Leafet.
Which one is the best for this use case? Is one faster than the other?
Geoserver is an OGC compliant Web server which can serve out data in OGC's web services, namely WMS, WFS & WCS.
You want to get GeoJSON Tiles, and use it in your Leaflet Map. GeoJSON tiles are not a OGC standard, and GeoServer can not serve out GeoJSON Tiles.
TileStache on the other hand, can serve out GeoJSON Tiles from ESRI Shapefile, PostgreSQL, MySQL, Oracle, Spatialite and GeoJSON data sources.
You can have your data in one of these formats/Databases, and then serve out vector tiles using TileStache.
This is an article I found with a quick Google Search, which shows how to serve out Tiled GeoJSON: TileStache: Generate [Topo|Geo]JSON Vector Tiles
You can show these GeoJSON tiles in Leaflet with a plugin like leaflet-tilelayer-geojson