There is no doubt the Black is the best not just in stills but it also has a better processor and better low light performance. The old Hero HD is basically the White and the Silver fits in between. If you don't want to film in full HD (takes alot of computer power) no point going the black. The remote works on all three cameras.
I always shoot in 1080 x 50p (that's Full HD at 50 frames per second and is PAL format,60p in NTSC) the white can't this only 720 x 50p but the silver can. The reason I shoot in this is because I mix shots in with my other pro cameras. You really don't need to shoot on these settings to get really good footage. The 50p setting is what will give the smooth slomo when you slow it down without using additional software. If you just want to post vids here on the Breeze without slomo 720 x 25p is fine. No need for the Black to do that.
I also have a Sony Action cam and the Ion , they won't match the Black. Sony costs the same as the Black and the Ion is about the same as the White cost wise and performance wise. Both the Sony and Ion have serious focusing issues underwater , the way Gopro has solved this is the new flat lens .Both the Sony & Ion have round lens and thats why they can't focus properly underwater. In summary if you can afford the Black buy it , it's the best but if bucks are tight the Silver or White are both great cameras.
Here is a couple of videos test videos I did to compare the White vs the Black at the same settings.The first is the white shot in really good light the second is the Black shot in late afternoon , the White would have grained out in the second video.
P.S I have nothing to do with Gopro.....
Gopro White 1080 x 25p
Gopro Black 1080 x 25p