I've heard there are a number of slight differences between these two similar fonts, is one better than the other for different contexts?
As far as the difference goes, you are right. There are some character which are slightly different however the difference goes way beyond just the comparison of the character.
Here is some explanation on ilovetypography
Yes, one is better than the other, for all contexts. The answer is Helvetica.*
I find the differences in uppercase CGQR and lowercase a and t the easiest to spot. And the Arial numeral 1 is gawdawful.
*Before people jump down my throat, be aware my tongue is in cheek. You may make a slim case that Arial is better for web design because it is more ubiquitous and has wider support. Otherwise, get outta here.