Three days after purchasing my 2001 TT, I had acceleration problems too. Felt like the car had lost 25-40% of its power. Turns out the airflow mass meter had failed. A mate's TT, same age, also had the same prob. Spoke to a dealer and it is something that tends to go.
Also check your lamba probes, ( to do with the cataylatic converter), they can also be prime suspects as if they are giving problems they lag behind during exhaust and starve the engine.
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