Liquidity vs. Lower Fees
Both GLD and IAU are doing the same job—tracking the price of physical gold that's sitting in vaults.
The main difference comes down to cost and liquidity:
GLD has a higher expense ratio at 0.40% compared to IAU's 0.25%, which means over time IAU will cost you less in fees. GLD is the OG gold ETF (launched 2004) and is massive with around $96 billion in assets, while IAU came a year later and has about $43 billion. GLD also trades at a higher share price—roughly a tenth of an ounce of gold versus IAU's much lower price point.
The performance is virtually identical. So you choose between higher liquidity and lower fees.