I'm not sure WOF They seem to start from a different proposition and mean different things. I may be misinterpreting but here is what I understood the expressions to mean:

A steel fist in a velvet glove.
I think this expression is akin to "you get more flies with honey than with vinagre". People will respond better if you deal with them kindly, so a hard/tough person (the fist of steel) will get more done if he directs with a velvet glove (the honey).

Speak softly but carry a big stick seems more like a tactical expression. There is no need to yell when you've got a arsenal to back you up. So if you speak softly, you sound more rational and maybe things will go your way BUT some people don't want to listen to reason so it is important to have that arsenal.