It really depends on many things. If you want purely the best OC then yes the HD7870 is the better option.
REQUIRED cooling is not really the way to ask this, get the best you can afford and you will get the best OC possible from that cooling. Unfortunately you could spend hundreds of dollars on cooling and keep the card cool but because it uses cheaper parts or the chip just won't go as far it won't OC as much.
There are 3 cooling option.
1. Water(custom loop)= very expensive
2. A card with really good cooling out of the box = usually the cheapest.
3. Or you can get aftermarket air cooling.
1. Custom loop - http://www.tomshardware.com/forum/277130-29-read-first-watercooling-sticky
2. An HD7870 with really good out-of-the-box cooler(not as good as aftermarket) = http://www.newegg.com/Product/Product.aspx?Item=N82E16814202010
3. Example of really good aftermarket air cooling = http://www.thermalright.com/html/products/vga_cooler/spitfire.html
Please note those are just example.
I would just suggest getting an HD7870 with decent cooling out-of-the-box, the HD7870 is a great overclocker even with stock cooling.