First of all, I do enjoy pvp but mostly on the ground. Why not in space? I GET CANNED LIKE FIVE SECONDS INTO BATTLE! Ok, so I need a faster computer and better video card, but even when I have perfect quality, someone fires on my shields with cannons and my hull is down to zero in 2 seconds. Dang. hate it when that happens. Anyway, I have tried fighting with beams, I never can penetrate shields! I have tried a cannon rapid fire with my Chel Gret, never works. Still the Defeated! screen. Ok, one more must I do? Even people with beam attacks destroy me. Requesting immediate assistance! (I have noticed carriers work well, but I don't have easy access to one on Fed character)
Shields won't save you all by themselves, not unless you've got ridiculously high innate resists somehow.
I'm assuming you're not using defensive skills. A simple combination of Tactical Team 1 + Emergency Power to Shields 1 or 2, and maybe even a hull resistance buff, will generally keep you alive in combat unless you're being focus-fired. That takes a little more skill to survive.
If you're wandering around relying on manual re-routing of shields and little or no shield heals/buffs, you're gonna get torn to pieces in PvP.
pvp is not pve, what work in pve often do not work in pvp... It's not only a matter of equipment but your overral build (skill and abilities). Moreover I think your ship is not the best choise for pvp because your turn rate is a bit low and the boff layout is not optimal (for a tact/tact toon who should have dps and manoeuvrability). A fleet patrol escort or a charal are better... May be a different destroy is also good, but my tactical toons only use escorts.... so I can help you only about escorts.
I'm not sure how to attach something, but my current armaments of the Chel cruiser are 2 Polaron dual cannons, 1 dual heavy polaron cannon, 3 turrets, a tranphasic torp launcher, and a transphasic mine torp.