FumbleFingers commented:
They're equivalent and interchangeable. The only real difference is that historically,
Brits used to favour downwards
but
Americans always liked downward better
– and we're falling into line now.
... which is the same with, for example, backward/backwards,
forward/forwards, upward/upwards.
But (rather curiously, imho) it's markedly "American" to use anyways
instead of anyway as a colloquial "interjectory conjunction".
...
I think Americans are more likely to adopt "folksy regionalisms" into
mainstream colloquial contexts (usually, with a degree of
"facetiousness"). So besides anyways, you'll often hear anyhoo (from
anyhow, which I think was originally a Scottish dialectalism, but I
haven't checked).
I'd add that 'upwards mobility' is far rarer than 'upward mobility' even in the UK; this (dropping the s) is probably the case with other strong collocates/compounds (forward thinking; backward-looking ...). [EA]