Interesting question, but not yet so many answers. I guess, that this is due to the likely fact, that not so many people have deep insights and personal practical experience with both solver systems.

If I had to chose, I would prefer ANSYS CFX because of it's unparalleled solver stability/robustness and the consistent and easy-to-use CFD workflow which it provides to CFD practitioners. This makes it a very reliable tool, where most of the time the user can expect to achieve a flow result in a foreseeable timeframe (which is usually not the case with ANSYS Fluent due to the embedded trial-and-error workflow with too many exposed numerical solver parameters of sometimes not very transparent influence on the solution process and results accuracy). Unfortunately ANSYS has decided not to put so much development effort into this solver anymore... But for the cases for which CFX is providing the appropriate models (like turbomachinery, turbulence, Eulerian multiphase) I still enjoy using it and will continue to use it as long as ever possible.

I think it really depends on which kind of problems you want to solve, as most codes come with a very specific background, and were then generalized to become general-purpose codes.

I work in the field of industrial combustion (e. g. furnaces in manufacturing industries) where FLUENT is the code that is most commonly used. Some industries have also developed their own, tailor-made CFD codes: in the glass industry, highly specialized codes such as GlassServices or CelSian's GTM-X are actually more common than general-purpose codes.

For turbomachinery applications, CFX is very popular, as Thomas already said. As far as I know, in the automotive and maritime sectors, Star CCM is more common than either Fluent or CFX, but I'm not that familiar with that field.

Generally speaking, most modern codes can cover a wide range of very different applications, but there is a lot of history involved which explains why some codes are more predominant in some applications than others. Of course, this is, to some extent, also the users' "fault" because they don't want to learn new work-flows or methods. They (and I definitely include myself here) want to stick with what they know works for their problems and tasks.

I agree that is quite difficult to give a definite answer. Formally, at the same accuracy order, on the same grid, at the same numerical precision any consistent and stable method should converge to the same solution. That can be observed in specific simple test-cases. In the real word of CFD there are so many additional issues that one should focus the comparison between codes only for a specific flow problem to have some useful assessment.

Some years ago we did something about such comparison of codes for a specific problem.

Conference Paper A comparative test for assessing the performances of large-e...