Added benefits include:

Complimentary Platinum Medallion Upgrades - 6 one way worldwide
Priority Baggage Handling
Complimentary Crown Room Club Access
Access to International Airport Lounges
Inflight *VIP Travel Assistance
Platinum SkyTeam Benefits

I am gold with Amex Platinum card so I have Delta Crown Room Access. When flying BC or F internationally I have lounge access. When flying coach internationally on another skyteam members metal, I am out of luck.

Also, you get a higher upgrade priority. I have been beat out by a platinum before.

Now, question is how do you travel best. If gaining status on another airline makes sense, go for it. The 6 free flights plus lounge access and higher upgrade status may easily be offset by rights on new airline.

I have US Air status and am flying United to SFO. I was able to get my wife and myself into E+ seats that way vs fret over a Delta upgrade on a really cheap ticket.

Good luck.