Benchmarking with V8
[n 5], (old-integer? n), 1000000 runs, 0 msecs
[n 5.5], (old-integer? n), 1000000 runs, 0 msecs
[n 5.0E300], (old-integer? n), 1000000 runs, 0 msecs
[n ""], (old-integer? n), 1000000 runs, 0 msecs
[n 5], (integer? n), 1000000 runs, 0 msecs
[n 5.5], (integer? n), 1000000 runs, 0 msecs
[n 5.0E300], (integer? n), 1000000 runs, 0 msecs
[n ""], (integer? n), 1000000 runs, 0 msecs
Benchmarking with SpiderMonkey
[n 5], (old-integer? n), 1000000 runs, 0 msecs
[n 5.5], (old-integer? n), 1000000 runs, 0 msecs
[n 5.0E300], (old-integer? n), 1000000 runs, 0 msecs
[n ""], (old-integer? n), 1000000 runs, 0 msecs
[n 5], (integer? n), 1000000 runs, 0 msecs
[n 5.5], (integer? n), 1000000 runs, 0 msecs
[n 5.0E300], (integer? n), 1000000 runs, 0 msecs
[n ""], (integer? n), 1000000 runs, 0 msecs
Benchmarking with JavaScriptCore
[n 5], (old-integer? n), 1000000 runs, 0 msecs
[n 5.5], (old-integer? n), 1000000 runs, 0 msecs
[n 5.0E300], (old-integer? n), 1000000 runs, 0 msecs
[n ""], (old-integer? n), 1000000 runs, 0 msecs
[n 5], (integer? n), 1000000 runs, 0 msecs
[n 5.5], (integer? n), 1000000 runs, 0 msecs
[n 5.0E300], (integer? n), 1000000 runs, 0 msecs
[n ""], (integer? n), 1000000 runs, 0 msecs

changing the behavior of integer? outside of a more comprehensive numeric discussion is low priority. The current implementation is already suboptimal in its coercion of numbers to strings.