Correction, anything big that isn't a paragon. That being said frigates usually lack the punch to take down bigger ships and/or carriers. Especially since in the latter case since fighters WILL swarm and annihilate you.
Only if you're running with full fleets each. Solo, most stuff bigger than you can beat you at the race to overload game, unless you manage to outrun their shields without taking more damage than you slip through.
I will say that most NPC frigates have more kinetic and fragmentation than explosive, and kinetic weapons are the longest ranged small ballistic weapons. So it really shouldn't be a race to overload since you should never get close to an NPC frigate except on your own terms. You basically want to kite them while turning your shield on and off, using your larger weapons to build up hard flux/armor breakdown, then when the enemy is weak bum rush them before they can retreat in to the horde. Target the flanking enemies since they'll be the most isolated. Hard flux is the enemy here, it should never go above half because you need to be able to active vent all your flux in a couple seconds (ideally faster than it would take for a rocket or SRM to reach you). For this same reason you shouldn't need capacity against smaller ships, only against larger ones.
You shouldn't bring any missiles that aren't reloadable (least not for killing frigates), and you should focus most of your OP into upgrades that make the ship passively better in brawling (hull strength, weapon/engine survivability, weapon range). Combat skills are very very important for flying frontline big ships. The most important upgrade for this style of combat is the one that makes armor protect the hull almost 100%, with that you should be able to negate small ballistic kinetic/fragmentation almost completely, unless that side of your ship has already been hit by a rocket or something. The other important upgrades are weapon damage, range, the maneuverability/speed stuff, and the tougher weapons upgrade. If you're not using escorts the PD upgrades and the "enemies do less damage if they're using the wrong weapon type" upgrades are essential, otherwise you should be OK without. Oh and insulated engine assembly is the best upgrade ever, you should put it on all your ships even the civilian ones.