I have both and prefer the Cinch. It is easier to punch and I like being able to choose the holes I want punched. You can use it right out of the box without reading instructions. I have not gotten the hang of the BIA. I can never get it to punch straight even with the little spacer thingy. The Cinch costs more, but it is worth it IMHO.
I have a bind it all and its difficult to line up. At work we have a cinch and all the ladies say it is way more user friendly. The fact that you can choose which holes punch is a major selling point. If I didn't already have the bind it all I would get the cinch
Oh, and yes, they both use the same wires. I usually buy the BIA wires, because they are a bit cheaper and I can get a box of 6 at HL and use a 40% off coupon, thus saving 40% on all SIX. HL also sells cinch wires, but in sets of TWO. which means a 40% off coupon will only save on TWO wires.
Cinch wires are great for a special color that you will not use as much of though,,,,,like pink or purple.