Old Spice and Speed Stick do absolutely nothing for me except produce more B.O. I don't have sweat ring problems so I've never used Mitchum or any other kind of anti-persprant.
I use Right Guard Sport deodorant or sometimes Adidas Sport stick deodorant. Works like a charm.
I have a friend who, despite being about 6'1" and weighing about 89 lbs, sweats like Sooner in a spelling bee. He swears by the Mitchum deodorant/anti-perspirant cream.