I think that "old" should not be a factor in performance. Tired in this context would equal poorly maintained. I am not familiar with the 3 year C of A standards of the UK. I am aware though, that if the aircraft is being maintained as specified by it's manufacturer, it will be having inspections at intervals of about 100 hours, which will include a check of engine cylinder compression, mag timing (the two of which are probably the fastest ways to get an engine to preform less well), as well as rigging, and other defects which could rob performance. Waiting three years to inspect for these defects is just poor. and it's certainly is well within the scope (and responsibility) of the pilot to satisfy him/her self that the aircraft has a record of suitably recent maintenance, to cause the pilot to believe that such defects would have been caught.
A part of the process which is involved in the setting of maintenance intervals by manufacturers is the evaluation of the lenght of time a defect could safely go undetected, without causing a safety (performance) concern. 100 hours seems to be a general standard. Certainly annually is!
Think of an aircraft as a collection of parts all pulling together. The old aircraft could have a brand new engine and prop. I used to fly a Cessna 207 with more than 19,000 hours. Paint was smooth but poor looking. Excellent maintenance, zero time engine (though probably "old"), and prop. Performed beautifully during my many fligh tests, to as high as 17,500 feet in a hard climb.
Pilot checks the condition of the aircraft both logbooks and walk around, then flies it in accordance with the flight manual and good practice, and it's going to perform properly.
Pilot DAR