do you have any information on which fault codes where stored in the memory or if any warning messages were displayed in the instrument cluster?
It's going to be tricky to analyse their diagnosis without information on the fault codes or details on why the technician came to these conclusions.
The first diagnosis is perfectly viable. A clogged DPF can lead to a lack of power. But a clogged DPF can also be identified by monitoring the readings obtained from the engine's exhaust back pressure sensor. The technician should have taken note of these readings prior to the regeneration and then compared them to the readings obtained post regeneration. Only when comparing these can the DPF be replaced. It may even be necessary to attempt to regenerate the DPF more than once.
If it is then deemed necessary to replace the DPF (which isn't as common as most people might think) another back pressure sensor test should then be carried out to confirm that this was infact the original problem.
To then go on and say that the catalytic converter is the actual problem or part of the problem sounds a little like clutching at straws to me. A failing or blocked cat can be identified by monitoring the status requests of the various engine sensors via the testing equipment. Overall, i find it unlikely that both components have failed at the same time, unless the vehicle is very mileage.
What are the exact symptoms of the power loss please? When accelerating from standstill, under kickdown, when slowing and then accelerating away quickly etc?
Apologises, i've just noticed the mileage which is quite average so makes it even more unlikely. I hope that they are submitting a goodwill claim to BMW on your behalf dude to this and the age of the vehicle.
There will be a surcharge on the old DPF but even if you were to examine it there wouldn't be alot to see, but a comparison between the weight of the old one and the new one can give an idea of the amount of soot trapped inside.