Why are some pitot tubes more prone to icing than others? I understand that there were several cases pitot tube failure in a certain way.

The pitot tubes were clogged by ice when the airplane was in cold and wet conditions.
The remedy was to exchange the pitot tubes by a different model from a different manufacturer.  

As an example, there was an Airworthiness Directive (DGAC 2001-354) applying to the A330 and possibly others, explicitly requiring to replace the model installed when delivered by a specific other model. 

The A330 originally came with pitot tubes from Goodrich Sensors and Integrated Systems,  part number 0851GR. The Airworthiness Directive of 2001 required to replace these by pitot tubes made by Thales, part number C16195AA, or a specific, more recent model from Goodrich.

I assume all models from all manufacturers have the same basic construction, like all can be heated, for example.

What is it in the construction of the pitot tubes that makes the difference?  

Is it just a design flaw in the Goodrich series that was fixed later? Somehow I expect it to be something more general. Are there other manufacturers building pitot tubes with a similar flaw? (That would be a good reason to require replacement with a specific model.)
Actually the answer is quite complex, but essentially depends on the local aerodynamics, shape of the probe and the anti-icing power (heating).

Imagine an airplane flying around a cloud, it essentially approaches air with small drops of water floating around, those drops of water impact the pitot tube and some of them keep over the pitot tube surface.

Now, the key question is if that water will or will not become ice. That essentially depends how long the water keeps over the surface and the local temperature.

Keeping on the surface depends on the shape of probe and the local pressure. The water temperature will depend on a balance between the external temperature (also dependent on the local pressure) and the balance of power applied to the probe to avoid freezing.

So, the phenomena is quite complex and depends on all of these factors, and the potential case of pitot tubes prone to icing will likely being a condition unexpected and outside margins as all these factors are taken usually into account.