Good info here.
F-15 is an air superiority fighter, Foxbot is a strategic interceptor, in particular one designed to intercept the Mach 3 US B-70, which we never built beyond the 3 prototypes. The F-15 is more manueverable, but the Foxbat is way faster. The Foxbat doesn't turn very well, even at slower speeds just below Mach 1, where most dogfights occurr. Depending on how equiped, the Foxbat probably has shorter range eyes but longer range missles. They are so fast that intercepting them is very difficult. IIRC, the Israelies never managed to intercept and shootdown any of the Mig-25s which were making high speeds runs from Syria to Egypt (or vice versa). Although they didn't have F-15s at the time, nor AMRAAMS. A better combination than an F-15 and AMRAAM (slammer) would be an F-14 with Phoenix missles. The F-14 was designed as a Fleet Air Defense fighter, a mission with many of the same requirements as a strategic interceptor, save that the FAD fighter also needs the ability to loiter, which is part of the reason the F-14 has a swing wing. Only the US Navy, and maybe the Iranians, fly the F-14. (We, or at least I, don't know if any of the Iranian F-14s are still flyable, having been deliered before the fall of the Shah, the Iranian hostage crisis, and spare parts having become a tad hard to come by after the Iranian hostage crisis under Mr. Peanut)