Hey - I used this tool: http://raidbots.com/comparebot/4ee7c...10004b5#damage (Ultraxiton)
I used my own kill on Ultraxiton in the comparison of what should be optimum. Don't use the actual dps as a meassurement because of different raid buffs, legendary, tricks of the trade and maybe different glyphs.
Look at mind blast per minute, dot uptime and mind flay uptime. Don't take shadow word: death that seriously, cause it mostly depend on your healers and wether or not you use glyph of dispersion. But still your shadow priest friend didn't cast any shadow word deaths at all.
Other than a little less mind blasts per minute and no shadow word deaths, your two shadow priests performed almost equally on Ultraxiton.