This is what I found...
These are the two bottles side by side after taking from the cellar...

and another view...

The bottles were a bit cold so look a tad cloudy through the condensation. Nothing looks any different at this stage so I poured them out. On opening, the normal one hissed as expected whereas the full one hissed a lot less. I poured the normal one first followed immediately by the full one and this is what they looked like side by side (the full one on the right)

Here's another view...

As you may be able to see from the pictures, what immediately strikes is the difference in head, but you may have also noticed the difference in colour too. The head with the normal one was fluffy and light and creamy and exactly as you hope and pray for. However, the other one was disappointing and quickly fizzed away to nothing as we probably all expected it would.
After a minute or so...

The colour difference was really surprising though and was enough to give the impression of them being two entirely different beers. In fact, I had a few friends round and asked them to do a taste test to see which one they preferred and they were all easily convinced they were trying two different beers, all preferring the one on the left (the one with the gap). So did I.
I poured some of the beers into two other glasses to eliminate the chance of the difference being down to the glasses I used and as you can see, the effect was the same...

I then started drinking them both...

Again, the head of the normal one stayed with me all the way whereas the full one was flat and lifeless. The normal one had head left over at the end whereas the other one didn't have anything.

and all done...

There wasn't even a trace of any lacing throughout the full one's life...

So, there you have it. I've no idea what the science behind this is, but I do now know what I thought I always knew anyway - not to overfill my bottles. You might think you'll get more in your glass, but it will at best be more of what you don't want - flattish, unconditioned slop.