You have no 'direct' way to identify the version of ECW in ArcGIS.
However, you can try the indirect way.
First of all, ArcGIS DOES support ECW v2 very well, including directly loading into Mosaic Dataset. In other word, if your ECW files are in v2, it should work in ArcGIS 10.x ... Inversely, pretty sure that ArcGIS 10.x does not support ECW v3 at all.
Secondly, ECW v1 is the first release (ECW) before 2000, which was mainly for IWS (attachment - ECW v1). ECW v2 is a stable release from ER Mapper 6/ 7, which is competitive to MrSID (attachment - ECW v2). ECW v3 is one of three compressors (ECW v2, v3 and JP2) from ECW JPEG 2000 tool within ERDAS Imagine/ ER Mapper (after ERDAS acquired ER Mapper in 2007), which is mainly optimal for ERDAS Apollo...