Question: Some studies have shown that serif versus sans-serif on a computer display is not what affects readability and the practical differences between the two font styles are largely inconclusive.

I observed some designers prefer to use serif fonts only for titles or important elements and that make me ask: The font style on a CTA affect user's decisions?

Answer: 
According to [this](https://blog.kissmetrics.com/how-typography-affects-conversions/) post by Kissmetrics:

> 
> As far as research goes, there is no ironclad answer as to whether serif or sans serif is better. But, as far as general consensus goes, when it comes to reading online, sans serif typefaces are easier to read because they are simple and legible even in small sizes. This means people can spend more time focusing on the message than deciphering the typeface.
>  Sans serifs are recommended for the body of the copy and serifs for the title and subtitles.
> 
> 
> 

We can arrive a conclusion that sans serif typefaces are better for CTA moments, where people need to spend more on focusing on the message (and in this case, the message that your CTA trigger needs to give).
I think you're talking about an [article by Alex Poole](http://alexpoole.info/blog/which-are-more-legible-serif-or-sans-serif-typefaces/). Anyhow, it basically says the same as you: in the battle of serif vs. sans-serif, there is not a decisive winner when it comes to legibility. They both have their pros and cons.

But size does matter in this case.  

Sans-serif is better when using a small font-size, because serif fonts tend to "smear".  

And sans-serif is also better in big font-size, think huge, like in advertisement billboards. Sans-serif is more legible from a distance.

So when your CTA button is small or huge, a sans-serif font would be the better choice from a usability perspective.

But other than that I think it's primarily an aesthetic choice. Does it fit the design?  

We could say that when it doesn't fit the design, the design will look incoherent and that might affect the opinion of the visitor about the company causing them to abandon the site. They could be of opinion the company might invest as less thought and effort in everything they do as they did on the design of their website.