Z1*s and RE11s are both essentially competition street tires. They clear water well enough to drive on the street, but are as sticky as possible while maintaining a high enough wear rating to qualify as a Street tire for SCCA SOLO classing. The tread is as wide as possible for the sizing, again to have as much grip as possible while staying within classing specs.
Both are amazing tires. I have the RE-01Rs, the precursors to the RE11s, on my STI and they are incredibly grippy. I need to upgrade my pads because in 255 size they overpower my stock brakes. The Z1*s were made to be grippier than the RE01-Rs, and the RE11s were made to equal or beat the Z1*s.
Whichever you get, you'll be amazed by the grip available.
Just remember when fitting a set of these, they are about half a size wider than a regular tire. (i.e. a 225 is like a 230, a 235 is like a 240, etc) Calculate diameter the same, but make sure you have an extra tenth of an inch or so of clearance on the sides.