GeoWebCache is able to serve layers in the following three standards: TMS, WMTS and WMS-C. Is there any remarkable advantage in using any of them in particular within an OpenLayers framework?
WMS-C is the best supported and most mature, but it's a bit of a kludge overlayed on top of WMS to support tiles and it incurs some extra overhead from having to use world coordinate bounding boxes rather than tile coordinates.
TMS is fairly mature, and is specifically designed for tiles, but is not an official OGC spec.
WMTS is an OGC spec that is meant to replace TMS and WMS-C. It works purely in in tile coordinates like TMS (although it computes them differently) but has some additional capabilities that weren't in TMS, like GetFeatureInfo. It's comparatively recent and less used so its implementations are less mature.