Work out the differences and see which suits you best:
Aga is the more 'prestigious' of the two (the snob factor
)
Rayburn does not dismantle to move/install - the Aga does
Aga's have smaller ovens than Rayburn
Aga's come in 2 or 4 oven versions - also possible to get matching 'standard' cooker to sit alongside
Aga's will not run radiators
Older Aga's were built to run on solid fuel, so you
do have the option
if you can get hold of one in decent condition.
Rayburn's have the oven temp gauge built into the door
Rayburn's take up less room as are smaller on the exterior
If you want solid fuel, it's easier to find a solid fuel burning Rayburn
That's all I can think of off the top of my head.
Whichever one you choose - don't get a converted one - get one that was made originally to run on the fuel it takes.
Love them both, had them both
........and have an Aga right now.