The above pretty much sums it up ; I've had several of both series .
The W123 is more of a relaxed cruiser with a soft , wallowy ride with which they float along the road , soaking up bumps . They were like this from new and I suspect were designed to be this way at a time when MB were trying to make inroads into the American market .
The W124 , like the preceeding W114/5 series , has much sharper and more controlled handling , and is probably more suited to fast , everyday motoring in modern road conditions .
Assuming you are looking at six cylinder cars , a W124 with the M103 or even M104 will be noticeably more fuel efficient ( both will generally return low to mid 20's mpg ) as well as offering better performance than either of the six cylinders offered in the W123 , those being the twin cam M110 as found in the various 280 models , and the much older single cam M123 ( which was a thinly disguised development of the much older M180 which had been around since the 1950's ) found in the comparatively rare 250 - neither of these engines would generally break 20 mpg , with consumptions in the mid to high teens mpg being the norm .
The W123 is more robustly engineered , both mechanically and bodily , with everything having a greater feeling of solidity than the W124 ( but then people made similar comments about it in relation to the 114/5 series when the 123 came out , decrying the introduction of plastic door handles in place of nice , solid chromed ones etc ) . Alas , the earlier cars are now much older and , although well protected in their day , now have rust problems simply because of their age . Many things which break on W124's , just don't on W123's though ( window regulators being a good example , but if you compare the over engineered item from a 123 with the mass produced one from a 124 you will see why - I've replaced numerous 124 ones but never one on a 123 .
A 123 is a Classic car from an earlier era , which could still be used on a daily basis , but is more of a car to nurture and cherish and which will probably outlast you if looked after ; a W124 is more of a modern car , easier to live with on a daily basis , still has the potential to last many years , but not quite as solid and durable as a W123 , with more parts likely to wear out over a period of time .
Cheaper examples of the W124 are still comparatively plentiful ( with the very last Indian produced ones now only being 11 years old , as opposed to the youngest 123's being a quarter of a century old ( as , of course , are the earliest 124's ! ) .