There are a  misunderstanding regarding numerical methods in Fluent and CFX. Both works with Finite Volume Methods.

Fluent is a Green-Gauss Finite Volume Method with a Cell-Centered  formulation. Minimal Squares can be applied also on discretization.  

CFX is not a Finite Element Method, is a Finite Volume Method based on Elements - EbFVM, with a Cell Vertex Formulation.

In the Fluent the element is of Volume of Control, e.g. if you have a 1 million of tetrahedrons, you will have 1 million of volumes of control. While in the CFX the volume of control is assembled around the nodes. Each  element is divided in sub-volumes. The flux through each face is base on the nodal values of element. As in finite  element method a Stiff Matriz is assembled for each element, a Flux matrix is assembled fo each one. The discretazation is made by means linear shape fucntions, ( tri-lineaer in 3D). 

Once each sub-volume has it own contribution evaluated. Each node will accounting for each sub-volume around itself. and the real volume of control is assembled. 

The entire process need a connectivity table as in FEM to assembling the Matrix System. Once it is done, the solver can try to find a solution. 

Hence, in CFX, there are flux balances as in a classical undergraduate curses of FVM. But with the advantages of FEM regarding mesh conformation to complex geometries.

There a good collateral effect. The number of volumes of control will be next 1/4 of the number of elements with tetrahedral meshes. Because the number of nodes is the same numbers of volume of controls. With hexahedral meshes this ratio is next  1, so doesn't matter. 

The stencil is not the same. In the CFX the stencil uses all nodes around . all nodes that are part of each element that share the node where the assembling is made. 

Hence, sometimes of course. CFX differs of the Fluent results, but a with a little refinement, both give the same result. 

The solver of Fluent is more open and have more options of 'tuning', and there are the pressure and density based options.The coupled option is available also. In CFX the solver is almost locked and a pressure based solver, with some key parameters that permits a tuning, but they are not  on the eyes. see " Expert parameters" carefully. The solver is very robust and rarely needs to have its default parameters changed. But same times the convergence is achieved only with these options. 

Residues is relative to each solver. Which is GOOD in CFX is not always GOOD in Fluent depends on the case. 

Both are good choices and choose which you feel a friendly and easy work with your research. 

There are a  misunderstanding regarding numerical methods in Fluent and CFX. Both works with Finite Volume Methods.

Fluent is a Green-Gauss Finite Volume Method with a Cell-Centered  formulation. Minimal Squares can be applied also on discretization.  

CFX is not a Finite Element Method, is a Finite Volume Method based on Elements - EbFVM, with a Cell Vertex Formulation.

In the Fluent the element is of Volume of Control, e.g. if you have a 1 million of tetrahedrons, you will have 1 million of volumes of control. While in the CFX the volume of control is assembled around the nodes. Each  element is divided in sub-volumes. The flux through each face is base on the nodal values of element. As in finite  element method a Stiff Matriz is assembled for each element, a Flux matrix is assembled fo each one. The discretazation is made by means linear shape fucntions, ( tri-lineaer in 3D). 

Once each sub-volume has it own contribution evaluated. Each node will accounting for each sub-volume around itself. and the real volume of control is assembled. 

The entire process need a connectivity table as in FEM to assembling the Matrix System. Once it is done, the solver can try to find a solution. 

Hence, in CFX, there are flux balances as in a classical undergraduate curses of FVM. But with the advantages of FEM regarding mesh conformation to complex geometries.

There a good collateral effect. The number of volumes of control will be next 1/4 of the number of elements with tetrahedral meshes. Because the number of nodes is the same numbers of volume of controls. With hexahedral meshes this ratio is next  1, so doesn't matter. 

The stencil is not the same. In the CFX the stencil uses all nodes around . all nodes that are part of each element that share the node where the assembling is made. 

Hence, sometimes of course. CFX differs of the Fluent results, but a with a little refinement, both give the same result. 

The solver of Fluent is more open and have more options of 'tuning', and there are the pressure and density based options.The coupled option is available also. In CFX the solver is almost locked and a pressure based solver, with some key parameters that permits a tuning, but they are not  on the eyes. see " Expert parameters" carefully. The solver is very robust and rarely needs to have its default parameters changed. But same times the convergence is achieved only with these options. 

Residues is relative to each solver. Which is GOOD in CFX is not always GOOD in Fluent depends on the case. 

Both are good choices and choose which you feel a friendly and easy work with your research. 

Dear Ricardo. I can not add anything to your pedantic explanation. I believe that Ehsan agree with my opinion.

Dear Ricardo. thank you for your detailed response. I have nothing to add to what you said except that I find Fluent in  combustion case is more powerful : in combustion models or in the libraries of chemical reactions (Reaction Mechanisms). But, CFX is very advanced in the field of turbomachinery respect to Fluent. Good luck in your research.

Dear Alliche, yes,  there are some advantages between them, as you correctly pointed out. Generally, they are regarding to be easy or  not to  do a specific set up, that is, a friendly pipe-line from the physical setup until post processing; or to have  a model implemented and well compiled and tested with realizable  results which avoid a UDF or a  FORTRAN coding. Moving mesh is other feature that differs.

Once Fluent became part of ANSYS tools,  some features  are been merged from CFX to Fluent and from Fluent to CFX in the new releases. The changes  have released very fast year after year , and with drastic impact. The version 12 both starts to  walk side by side, but each one  retain some key features as you mentioned. Fluent now is able to run in GPU. CFX this feature is not available yet. 

Concerning  numeric kernel, the solvers,  both are very  robust. 

Please, have a look a little more about problem of ANSYS CFX.

Hello Ricardo Vicente de Paula Rezende . Very helpful answer. I'd just like to know: how do you know that CFX is uses a pressure-based solver? Is this information somewhere in the documentation?