Profit on cost
A single number on the whole project. It tells you what the project earns relative to what it costs. Most useful when comparing schemes on the same site.
Equity IRR
An annualised time-weighted return on the equity you put in. It captures timing, so a faster delivery improves IRR even when profit on cost is unchanged.
Which to trust
If profit on cost and IRR move in the same direction, the answer is clear. If they disagree, the difference is timing. Look at the cashflow to see when capital is in and when it comes out.