is it safe to say under equity method, 100% consolidation and proportion method the equity is the same, but if it is less than 100% consolidation there is extra minority interest, thus it has higher total equity?
If you mean on acquisition method, it’s not the same. Under acquisition method by consolidation, BS and PL positions are merged and intercompany transaction are cancelled (offset) in consolidation report. Intercompany transactions are shown in separated reports. Under equity method only proportionate share in associate is shown in BS while income/losses from investments are shown in P/L.
Also, according to GAAPs, equity method must not apply if parent has full controll under subsidiary.