The USS Reliant which is a Miranda Class (Wrath of Khan) is a lot more heavily armed than a Connie. It not only has the same phasers on the saucer section as the Enterprise but it also had external phaser pulse cannons and both fwd and aft firing photon torpedoes on the exterior pylon where the Enterprise only had fwd torpedo bays. They both had spec 7 main phasers on the saucer section so they were even there so if their shields were comparable (and they should be) then the Reliant (Miranda Class) should take out a Connie as the Reliant can fire both phasers and torpedoes both fwd and aft and the Enterprise cannot.
Someone on here said the Reliant only carried about 20 crew members, thats not true, thats about how many Khan had in his group on the Reliant but the Reliants normal crew was rated at about 240 officers and enlisted.
I'm new here but i've been a Trekie a long time, I watched the original ST with Shatner, Nimoy when it originaly aired on tv.