Both will leave a completely dry cider, unless your sugar levels are really high or you stop fermentation in some way (see below). The simple sugars in apple juice are easily metabolized by yeast, unlike the complex sugars in wort, so attenuation is 100%.
Many people report good results from Nottingham, but my experiments with it didn't impress me enough to keep using it. Can't remember if I ever tried American ale yeast, but I wouldn't expect much from it. The "clean" flavor profile means it won't contribute much to the finished cider, and it is likely to ferment out most of the aromatics and flavor compounds.
Nottingham is said to be rather temperature-sensitive and can perhaps be used to produce an off-dry cider, by crash-cooling and racking off when the SG is around 1.01 or so. Ferment at 65F and chill to 32F, yeast should drop out. I think I did this once and it worked, but haven't bothered to do it again.
