Formica and laminate are the same thing. Formica is just a brand of laminate.
If you're after something typical, like black, Home Depot will have it in stock - no special order necessary. I don't think it's too much more expensive than paint, but remember to factor in the cost of other materials. You'll need a gallon of contact cement if you're doing an entire cabinet. That'll run about $15. Plus you'll need a disposable paint brush (trust me, you'll never use it again) for applying the contact cement. You'll need at least five or six dowels, so that'll be a few dollars. You also need a j-roller, but the rolling pin in your kitchen works fine if you'd rather save some money. Also, if you don't have a flush trim or template bit for your router, that'll ding you for another $20. But seriously, if you have a router but don't have a template bit you don't know what you're missing. You need that regardless of whether you laminate your project. At any rate, you can't apply laminate without it.
I'd say applying laminate is actually less work than doing a good paint job with multiple coats and sanding in between. Considerably less work even. You just score it more or less to size with a untility knife, leaving at least 1/4" overhang (I usually make it more like 1/2"). Slather some contact sement on both surfaces. Lay down the laminate, then run the router around the edges. And you're left with a flawless surface you could never reproduce with paint and it's WAY more durable to boot.
edit: spelling