That's a problem with having PvP gear that is higher in item level than your PvE gear. Basically you bought a piece here or there with honor and got a lucky drop out of VoA perhaps, but those pieces are well beyond your current level of progression. You should be running heroics and tier 8 level content at your current progression level, but buy and win tier 10 equivalent PvP gear. Your PvP gear looks better because it is several tiers higher than PvE gear options you have. However, you are no where near prepared to actually be raiding in tier 10.
Your first bet will be to grind heroics and buy mostly the tier 9 pieces in order to fill in gear gaps. Once you have those you can probably start running ToC25 and ICC10 to get either upgraded tier 9 pieces while working on your tier 10 as well.
"In anything, if you want to go from just a beginner to a pro, you need a montage." /w TankSpot WTB Montage for Raiders.