I have both and use both just for a few days. In normal quest Petra is slightly doing better. But same as other 6*, Petra's and Ana's power are far beyond the challenging of the quests.
In boss battle, it depends on types of monster. I think Petra is slightly more versatile. BUT since we do not send one character to deal with boss. It makes no different.
For arena, where the highest attack power counts, ANA WINS.
To summarize, I my opinion, all 6* are overpower for everything. Every 6* will do fine in any activities....
EXCEPT in the PVP arena event.It is the only place that each 6* will shows its true value. Highest attack power, fastest speed, appropriate skill, low deployment cost, these will make it outstanding.