Something which is up for grabs is free to be taken by anyone. Example: "I don't want my baseball glove. It's up for grabs." Reply: "I'll take it!

Something is up for grabs when it is up in the air and can be taken (grabbed) by anyone. Example: "Are all of the seats taken" Reply:"No. Some are still up for grabs."

You must act quickly if you want to get the thing that is up for grabs, because it could be grabbed by anyone. Example: "Yes, a few seats are still up for grabs, but you had better act quickly. They're being taken fast."