Of course there is a speed difference between the two, it's in their name: 1066 DDR operates at 1066 MHz, while 1600 DDR operates at 1600 MHz, so it is 50% faster.
These are the maximum speeds at which these two memories can operate: if you insert a 1600 DDR bank in a slot that is clocked at 1066, it will work at the reduced speed, and you will have wasted your money.
Also, just to be complete, in truth these chips work at half the frequency quoted above. However, they transfer two data units per clock cycle: this is the meaning of the first D in DDR: Double Data Rate. In other words, they are twice as fast as SDR memory (which, I bthink but am not sure, is not used in pcs any more). Because of this double efficiency, their quoted cycle is twice the true clock speed at which they work: in other words, 1066, 1600, and so on are the effective data transfer rates achieved.