I'd choose the Black (and have!) for that warranty; not just for its length, but because it wasn't cut back. Many other drives have had their warranties REDUCED, which does not inspire confidence in materials and/or methods, either or both of which may have changed to cut costs (by cutting quality).
My Intel rig ("Phoenix") and my wife's rig ("Greenhouse") both have RAID1 pairs of WD Black drives in them.
Edit: OTOH, my AMD rig ("Omega") has a pair of 2TB Seagate "LP" drives in it, bought before the flood and before warranties were chopped.
The Green is a considerably slower drive. If you don't need the speed, then go for that one. I always lean towards speed for drives as they are the slowest part of a system. A longer warranty is nice too.
Depends on what you're storing. If it's media files, go with the Green drive, as capacity is king. If it's going to be storing commonly used games/applications, do yourself a favor and get the Black. The higher load on the drive will make it more likely to fail, making that warranty a very nice perk, and the drive is much faster so your applications will load more quickly.
The Blacks I have (in pairs, so noise is doubled too) are near-silent. This is an improvement over the first Black drive I ever got, which was the noisiest drive I've owned (but not intolerable). They now seem to be as quiet as any other mechanical drive I have.
I wouldn't make this too hard. Both drives are good choices. Go with your gut, and either way, you will be good to go. Still, hard to say no to 1.5TB of storage at $50. That is a heck of a bargain. In 2 years, you'll be looking for an even bigger drive anyway. Don't let the warranty distract you too much.