Auto sync is turned on in both devices but nothing shows up on the Nexus 7 unless I manually transfer pictures via bluetooth. Notably, Calendars and People sync without a problem. But not Gallery. My phone is a Galaxy Nexus. Both devices are running Android 4.1.1.
AFAIK, pictures from gallery are not uploaded to picassa gallery by sync, unless you intentionally upload them by sharing options.
To put this to test, I just now tried to capture an image though camera and synced. It did not turn up in Picassa.
I don't know why this way, but on the first hand if your first device is not uploading image to picassa with sync, there is no way your other device is going to get it.
There are plenty of other ways using apps like sugar sync, drop box etc. but I assume here the question was asked in compassion with contacts and calendar which gets synced with Google's services without any other app support.