As long as you use a lower profile tyre 40 for 16" then the overall diameter wil be the same as a 15" with a 45 profile.The ap calipers look like this.
Some years back I messed around swapping wheels around on my escort and the larger wheels on land rovers...I found it changed the reading on the speedo ....in my case it was 10mph out...not sure what to expect if you were to go from 15 inch to 16 inch rims...I'll leave that for another member to answer.