After further reflection, I may have been half right and half wrong with that posting. Here's what they will do that ESU's won't. As an example, I have a Zimo-equipped loco with a gyralite on both ends that can be turned on and off independently. When you turn either of them on, the cycle starts at the beginning regardless of where the other one is in its cycle. The actual tempo is the same, but where there are in the flash cycle is completely independent from the other. With ESU's, the effects are tied to what is set in the programming and, while you can offset flashes between effects with "phase shift" (V5's) or "opposite phase" (pre-V5's), will return to the same exact pattern until the programming itself is changed. So, with an ESU decoder with no phase adjustments, the gyralites would always flash at the exact same time regardless of if they're turned on independently. With the Zimo's, it's different every time you cycle one off and then on again. Hope this makes sense.
