Tides are caused by the Moon's gravitational pull (and its mass), not what it's made of per se — composition only matters because it changes the Moon's mass (and thus gravity) for a given size.
The Moon's average density today is about 3.3 g/cm³ (mostly silicate rock, with a small iron core). Iron's density is about 7.9 g/cm³ — roughly 2.4x greater.
If the Moon were the same size (same volume) but made entirely of iron, it would be about 2.4x more massive. Since tidal force scales with mass, tides would be roughly 2.4x stronger — higher high tides, lower low tides, and stronger tidal currents.
A few other effects to note:
- If instead the Moon kept the same mass but became iron (and thus shrank in size), tides would be essentially unchanged, since tidal force depends on mass and distance, not composition or size directly.
- A much more massive Moon would also change the Earth-Moon system's dynamics over time (orbital distance, rotation rate, day length) through greater tidal friction, but that's a longer-term effect beyond just "how big are the tides right now."
- The Moon's iron core wouldn't affect its gravity from a distance anyway — gravity depends only on total mass and distance, not on internal structure or arrangement.
So, the short answer: an all-iron Moon of the same size would pull noticeably harder on Earth's oceans, producing significantly bigger tidal ranges.