Tho I do have the Pro version and not Player, I will speak from VMware in general prespective vs Virtual Box.
For Linux Guest OSes, VB is more stable and offer better performance. Also easier to install Guest additions in Linux.
For Windows Guest OSes, VMware takes the lead, as above mentioned, such as better host to guest integration, better graphics support (trivial I know but still a plus)
Now on both free versions, VB offers more quality of life options that you will only find it in VMware pro version. Another thing is its resource usage as well as running services. VB doesn't have any service until you actually run the software, while VMware has it constantly.