Thinking of replacing my Sync with one of these two. I assume that the No Rules would have a similar motion as the Sync [but stronger] because they both have an asymmetrical core, while the Haywire would be somewhat smoother and earlier because of the symmetrical core. Am I on the right track, or is there really not a lot of difference between the two? Thanks in advance for any input.

IMO the only conditions that warrant either of these two are heavy sport patterns.
I prefer the smoother motion of the Haywire.

You're about right OP.  But your sync probably has alot of games on it, and either the haywire and no rules will hook circles around it.

Nib vs nib vs nib the sync would fit in-between the no rules and haywrie.