The two profiles start under different circumstances.
1. EFTO: approaching the end of the runway, ground level, gear down, fixed flap setting until accel ht, probably reduced thrust.
2. EO GA: 2/3nm from threshold (potentially nearly 3nm before the EFTO point), 200ft agl, gear about to retract, flaps retracting to the GA setting and full thrust available.
So, while following the EOSID might be wise, it depends on the circumstances and may not be necessary.