I use both as heavily armed multi-role ships. Some days I want to fry some fools in a CZ, - either ship does well there when specced for combat, they both have advantages and drawbacks. The Cutter's greater boost speed makes it easier to disengage from hairy situations, the Corvette's higher maneuverability makes it awesome for fighting.
They're also both pretty great as armed traders, I can stuff hundreds of tons of cargo in either and still be able to smash any npc pirate daring to interdict me. Which of course I do, for the bonus money from the bounties.
I loathe mining, but I have done it in both ships.
Smuggling. Eh. No. Neither ship is great for that.
I've done a bit of exploring in the Cutter, got all the engineered bits for trying it in the Corvette too but haven't tried it out. Sure I'd be doing many more jumps, but I figure I'll get whereever I'm going eventually.
Both ships look amazing, and both ships require all the engineering, but the end result is so worth it I think. They're each fun to fly, if you can get past their quirks. (All the drift in the Cutter, and the slow boost speed of the Corvette)