Thanks for all your responses. In my case, I don't see a great conflict between them. The general impression is that the second teacher is picking up on things in more detail, such as phrasing, dynamics, etc. To be fair to my regular teacher, I have never indicated to him that I wanted to study pieces in great depth.
Another point picked up by the second teacher, which is potentially more worrying, relates to the my use of the damper pedal, which was not clean enough. I suspect it might have something to do with my regular teacher's piano, which by his own admission, is quite bad: for example you have to press the pedal about half way before the dampers move. I hate to think this might the cause and I don't want to come across as being too materialistic. Surely, you don't need to learn on a Steinway to be a good pianist?