DCT is a dual-clutch transmission and the Steptronic is just a high-quality traditional automatic torque-converter transmission. The DCT is a 7-speed and the Steptronic is a 6-speed. Both can be driven with paddle-shifters or in fully-automatic mode.
When it comes down to driving, I'd say the only big difference is the Steptronic shifts fast and the DCT very fast. There have been some quirks reported about the DCT that some people get annoyed with. I've driven both and both are impressive trasmissions. The DCT definitely shifts faster but I'm continually impressed with the shift speed and smoothness of the Steptronic.
Hope that helps!