I don't know the advantages of open play.
The modes are just means to filter players out.
Solo - filters every other player out, so it's basically a single player mode, but in a galaxy affected by everyone
Private Group - filters out every player that is not a member of that PG
Open - No filters except Block, which is a player custom filter which allows one to remove certain players from their direct gaming experience
That's just it.
Modes do not enable pvp, they just enable multiplayer.
Which multiplayer can be collaborative or antagonistic.
Now, multiplayer does have some advantages over Solo:
- wing trade bonuses, that's a small percentage trade bonus for the wing members
- combat bonds and bounties are given to all wing members present in the instance, so it may be eventually used as a credits Powerlevel mean
- shared missions, pretty much the same as above since one can take a wing mission, complete it solo, then invite people in wing and share the mission and give them free credits (or it used to work like that, not sure if FDev didnt fix this behavior)
- AX CZ gives credits to anyone that touches the Goids, no matter if the player is affiliated to the wing or not.
But all those advantages are valid for both PG and Open, it's a multiplayer thing, not an Open thing.
So, to conclude - the main advantage of Open over PG is the fact that it allows one to meet and play with or against perfect strangers in a free for all setup.
While the PG is usually used to play with friends or with guildies or to get players to play along in a certain format/ruleset
For example: Mobius PG was (is) a PG dedicated to PVE activities and in this PG all PVP is forbidden.
Same for Fleetcom although this PG is used mostly by explorers.
However, being in a PG doesnt mean one cannot engage in PVP. People may join a PG only with them 2 in it, just to have an uninterrupted pvp experience
Or, as it happened multiple times in the past, gankers have infiltrated into certain PG like Mobius or Fleetcom and murdered members of the said PG
The problem with the PG is the fact they have certain size limits, they usually have a rather complicated acceptance procedures which takes time.
So it's a very artificial and limiting environment.