  A comparison is presented of Sunyaev-Zeldovich measurements for 11 galaxy
clusters as obtained by Planck and by the ground-based interferometer, the
Arcminute Microkelvin Imager. Assuming a universal spherically-symmetric
Generalised Navarro, Frenk & White (GNFW) model for the cluster gas pressure
profile, we jointly constrain the integrated Compton-Y parameter (Y_500) and
the scale radius (theta_500) of each cluster. Our resulting constraints in the
Y_500-theta_500 2D parameter space derived from the two instruments overlap
significantly for eight of the clusters, although, overall, there is a tendency
for AMI to find the Sunyaev-Zeldovich signal to be smaller in angular size and
fainter than Planck. Significant discrepancies exist for the three remaining
clusters in the sample, namely A1413, A1914, and the newly-discovered Planck
cluster PLCKESZ G139.59+24.18. The robustness of the analysis of both the
Planck and AMI data is demonstrated through the use of detailed simulations,
which also discount confusion from residual point (radio) sources and from
diffuse astrophysical foregrounds as possible explanations for the
discrepancies found. For a subset of our cluster sample, we have investigated
the dependence of our results on the assumed pressure profile by repeating the
analysis adopting the best-fitting GNFW profile shape which best matches X-ray
observations. Adopting the best-fitting profile shape from the X-ray data does
not, in general, resolve the discrepancies found in this subset of five
clusters. Though based on a small sample, our results suggest that the adopted
GNFW model may not be sufficiently flexible to describe clusters universally.
