The one one the left appears to be an original Pektron/MG Rover or SAIC/MG Motor remote fob, and probably came with the car originally. The one on the right is a more recent XPart/Genuine MG Rover Pektron replacement (possibly the original was lost or damaged and needed to be replaced).
Whilst the internal layout of each is different, they should operate the same (and indeed it appears to have been doing so until now).
Have you tried swapping the battery from the working fob to the non-working one to verify that it is not simply that the battery has expired?
If it still does not work with a known good battery, it is probable that the SCU has 'forgotten' the last code for that fob. It is a known issue that the SCU sometimes 'forgets' some or all of its settings (including the fob rolling code) if it has been subjected to a reasonably long period of low power from a failing/discharging car battery. As you mentioned removing the battery to charge it up, I suspect that may be what has happened here?
There is no re-sync procedure for the Pektron type fobs; they should just work if the SCU has the correct code. Neither is it possible to read or retrieve the code from the fob to reprogramme the SCU to recognise it. If the code in either the fob or the SCU has become corrupted, the only solution is to get a brand new fob (complete with its initial barcode).
I am not sure who manufactures the current XPart supplied fobs, but it is clearly a different company from the one that manufactured the originals - and as they are also priced significantly lower than the original factory fit ones used to be, I wonder if they might be less robust, so it could be that the fob itself has failed (although it would be a bit of a strange coincidence for that to happen at the same time that the car battery was disconnected). ( I also note that the newer XPart fob uses a different sized battery cell, which will no doubt cause people some confusion in the future!)
Sometimes when the SCU doesn't re-initialise correctly after having the car battery disconnected, it can be worth trying to force it to reboot again by disconnecting the car battery again for several minutes and then reconnect. Others have found that this does sometimes rectify the issue (but it has been known to take quite a number of times repeating the procedure before it has the desired result.