There can be multiple advantages of using PROCESS macro over SEM like:

• Easy to use
• Many types of Models can be analysed by using PROCESS macro like (Mediation, multi-mediation, mediation-moderation, moderation-mediation)
• PROCESS is not needed to estimate the parameters of the regression equations, as this can be done with any least squares regression program (such as SPSS's REGRESSION command ) and the results will be identical to SEM.                                                                                                                                    * You have to cite some studies showing identical results in PROCESS and SEM (Hayes, 2013)
• complexity of drawing graphical model in SEM. However, PROCESS macro can provide results without drawing a path diagram.

More advantages can be found on Hayes (2013, pp. 161–162)

It depends on your research study that which technique suits your data and model. However, I prefer SEM using Amos as it deals with both observed and unobserved (latent) variables such as common factors and measurement errors. 

Andrew Hayes, Amanda Montoya and Nicholas Rockwood wrote a paper comparing PROCESS with SEM ("The analysis of mechanisms and their contingencies: PROCESS versus structural equation modelling", 2017, Australasian Marketing Journal, 25, 76-81) which might help. 

I think the subject of question is that PROCESS in SPSS use OLS while SEM has the option to use ML. And most of literature prove that ML is better than OLS. So, to tackle the question I suggest you make a stand that you had a strong result for OLS (e.g. sample size, normality of data, etc.).

There can be multiple advantages of using PROCESS macro over SEM like:

• Easy to use
• Many types of Models can be analysed by using PROCESS macro like (Mediation, multi-mediation, mediation-moderation, moderation-mediation)
• PROCESS is not needed to estimate the parameters of the regression equations, as this can be done with any least squares regression program (such as SPSS's REGRESSION command ) and the results will be identical to SEM.                                                                                                                                    * You have to cite some studies showing identical results in PROCESS and SEM (Hayes, 2013)
• complexity of drawing graphical model in SEM. However, PROCESS macro can provide results without drawing a path diagram.

More advantages can be found on Hayes (2013, pp. 161–162)

SEM is developed to cater for limitation in SEM especially when dealing with latent constructs. Move forwards instead of backward.

If you said the traditional regression is better than SEM, then you need to read this rejection letter from AMJ for articles using OLS instead of SEM.

We can use Hayes in case of observed variables having one moderation. However when we have latent variable or multiple moderators in the model then AMOS is preferred in the case of theory testing and SMART PLS is recommended in the case of Theory generation (development).

It depends on the discipline of study. Hayes' PROCESS has its own limitation, which most SEM can easily address. However, PROCESS itself its own merits that justifies its use over SEM. Prof Andrew Hayes himself strongly advocates the use of OLS regression over SEM (none of his articles used SEM).

PROCESS weakness against SEM

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1. If the specific independent variables has multiple dimensions (SERVQUAL, MARKOR etc), PROCESS could not analyse all at once. Only one exogenous variable can be entered in a single analysis.

2. The models that can be run using PROCESS is very much pre-defined (the models can be found in the appendix section of Hayes latest 2nd edition book), and you will not be able to draw the pathways just like in AMOS or PLS.

3. Complex serial multiple mediation is not possible.

4. Its not quite graphically intuitive to use.

PROCESS advantage over SEM

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1. Offers various complicated regression pathways that SEM programs do not offer (e.g. 2 moderators simultaneously, moderated moderation analaysis).

2. It is assumed that not all moderating effects are significant across all ranges of the moderator variable (continuous). PROCESS macro offers the Johnson Neyman method of visualizing the interaction effect by generating a series of plots that can be later assembled into a diagram/graph. The diagram depicts the conditional effect of X (focal predictor) on Y (dependent variable), as a function of M (moderator variable). The moderating effects are probed using the regions of significance in accordance to the Johnson-Neyman technique (Hayes, 2013).

Hence, PROCESS may be a suitable choice for research in which the variables are all directly measured variables (e.g. in clinical, health and psychological setting that employs hard data). Meanwhile, SEM is better used in research where latent variables are present (ie. factors defined by indicators, and involve soft data) which is widely used in marketing, information system and organizational psychology studies. Its also possible for marketing/organizational reserach to use PROCESS IF a there is a single Independent Variable (that is not multi-dimensional), and the proposed model fits with any of the pre-defined models offered by PROCESS.