Depending on how fast you are running your SPI communications, a simple potential divider will do the trick.
As for the other way around, it "may" work, if the 3.3v given out by the Atmel is within the Vih specification of the input to the LED controller chip - it will be specified in the data sheet. If not, then yes you will need some way of increasing the voltage. There are many options around, and many schematics and tutorials online.
Ask google - he knows.