If you're going to be leveling up the alt as well, I would say stick with Alchemy. Mining makes a lot of money as you level, but at least on my server it seems as though there are way too many high level miners out there. Stacks of herbs and even stacks of the new leather are going for twice as much as stacks of ore. So I dropped mining and went back to skinning/herbalism. It's working for me.
Also, alchemy can help you out with all the potions you make in addition to the money you make by selling them. If you find you are getting some use out of alchemy I would stick with it. If you're not using the potions you make though, you could consider picking up mining. It is a pain to go back and level it though.
I would check out the prices for high level herbs, potions and ore/bars on your server auction house before making any decisions though.