You may get away with keeping them if they are in good order.
BUT
Are they big enough to be run at a low enough temperature to allow the modern boiler to run in condensing mode, or will you be having to run them at 70 or 80 degrees to get the room temperatures you want? Not condensing = not (quite) as efficient. Modern radiators aren't inherently more efficient (unless you look at output per kg of steel used in their manufacture), but that doesn't necessarily mean the old ones are suited to a new installation.
Are the pipe runs truly suited for use with modern pumps, or will the pump need to be run at an unusually high pressure to force enough flow through them?
If they are big enough and the system design is acceptable for modern times, if you don't have it powerflushed, will the boiler suffer from poor system water quality? Equals less efficiency and shorter opertaing life. If you do have them powerflushed, then expect to pay at least £450 for this (should be a day's work and chemicals and equipment cost money). How much are new radiators again? How much is new pipework?
What it comes down to is how good an installation you want, and what the cost of cleaning or modifying what you have would be vs replacement. I'd say new radiators may last longer than the old ones, but I don't believe even that is necessarily true, though it may be in some cases. It isn't a simple answer because it will even depend how hard and disruptive a complete new system would be.
I think it comes down to what the companies are saying exactly.
