The Phase LED's will only show-up when you're in S0 (on) maybe S1; whereas the case's 'power on' LED are on S0-S4 and off S5 (off) non-S0 aka Sleep states it will probably blink on/off. Remember the 'Phase LED' should only indicate power to the CPU, and then it's a very poor indicator.
Gigabyte has more advanced MOBO's with all sorts of 'LEDS' e.g. UD5 and UD7 series. IMO the best are MOBO's those with BIOS Code indicators.
If the PSU is plugged-in, has power, but the PC is in the S5 (off) state no indicators driven by the MOBO will be on. In the off state very few PSU's have any indicators.
Again, the answer to your original question is the case's 'power on' LED.