The major advantages are in current draw. Higher voltage will equate to lower current draw. You will have more power for holding headspeed and your packs will fly for longer.
Downside, expense, the packs are a bit more expensive and obviously a 6s 5000 pack will be lighter than a 7s 5000. You can overcome the weight a bit by running slightly smaller capacity 7s packs as the extra voltage will lower the current needed for a given flight time.
Real world example:
My E7se 12s setup:
Rail 716
Scorpion 4530-500le
Castle EDge 160HV
BEC PRO
12s 4300mAh packs Opti Power Ultra packs
2050 rpm
Flight time right at 5 minutes with room left to go.
My E7se 14s setup:
Rail 716 F3C
Scorpion 4530-450LE
Scorpion Commander V 120HV
BEC PRO
14s 4100mAh Pulse Ultra Packs
2050 rpm
Flight time 5.5 minutes easy can go 6 but gets into overhead when I practice speed.
