Here's a few Lady Shiva bios if that'll help any:
http://www.unstable.com/whoswho/ladyshiva.htm
http://www.rapsheet.co.uk/RapSheetMain/Character.asp?UniqueId=100
http://www.dccomics.com/secret_files/dc_character.html?sc_dc_itemCode=ladyshiva
Elektra will win methinks. Shiva is more skilled in my opinion. She has on panel stated she learns something like 12 new arts a year and has demonstrated a ridiculous knowledge of nerve strikes/deathmoves over the years. Prometheus also stated she was the third best H2H combatant in all of DC.
However Elektra is also highly skilled and is also a top tier. She has demonstrated better speed feats and better durability. She is physically better with a really good level of skill and that is why she wins.It will be a tough fight though.