It all depends, Neil, on how you define a better job. The main ingredient is the technician. Presuming we're looking at a minimum of 100psi, then, everything else being equal, a 135psi pump will allow you to perfrom the job quicker. Most portables are restricted on power because you need to balance the water pressure AND flow rate with the available power for the vacuum. It may be necessary when the psi exceeds about 200 psi to reduce the size of the jets to limit the risk of over wetting the carpet. I know Cleancare International do this with their 400psi models.
Try not to think of cleaning carpets as being just the extractor machine. Good training and experience will tell you that the preparation of the carpet and soil is of probably greater importance. Your HWE machine then becomes just a tool for rinsing away the loosened soil. Most of the UK manufacturers will balance the pump with the vacuum and tooling. Just buy the most power your budget will allow. If buying secondhand, try to check if everything is as specified by the manufacturer, if not, come back for advice on adjustments required.
Safe and happy cleaning:)
Ken