Can I use my iphone4s charge cord for iPad and visa versa?

yes, you should have no problem using the charging cord for either device. I do that.

iPad charging iPhone works fine. Iphone to iPad not so much.

Check the power specs. the iPad charger is a 10W charger, I think the iPhone one is only 5W. Technically it will charge the iPad but it will take longer.

The iPhone, however, seems to handle being charged by the iPad's charger fine.

You can use the cable yes, they are the same. But the iPad's charger plug is twice as powerful as the iPhone's - so whilst an iPad will charge with an iPhone charger it will be a lot slower than with it would be with the iPad's own charger. You can safely use an iPad charger with an iPhone : http://support.apple.com/kb/HT4327