I personally take issue with using EITHER of them in the first damned place. jQuery is a fat bloated train wreck where pretty much EVERYTHING I've EVER seen done with it falls into one of three categories:

1) Stuff that would be less code as vanilla JavaScript NOT counting the framework size against the total.

2) Stuff that's HTML or CSS' job.

3) Stuff that has ZERO DAMNED BUSINESS ON A WEBSITE IN THE FIRST PLACE if you care in the slightest about semantics, separations of concerns, graceful degradation, accessibility, loading times, and all the other ENGINEERING concepts that should be an integral part of ACTUAL design.

React only takes the "scripttardery for nothing" idiocy and multiplies it, only further pissing on accessibility and usability from orbit, pissing off users by doing crap client side that to be frank, has ZERO damned business being processed client side.

Simply put, if you need JavaScript to build a UI on something built with HTML and CSS, you aren't qualified to be using web technologies and are telling large swaths of potential users to go **** themselves. More so the less the page is able to gracefully degrade when scripting is unavailable for security concerns, distrust, or even bandwidth restrictions. Not everyone lives in the magical fantasy-land of low latency high throughput broadband -- not everyone has the perfect vision and physical capabilities to use the garbage sites vomited up with the "I started with what it looks like" approach that has scripttardery slathered all over it with ZERO graceful degradation.

... and depending on the type of sites involved and the subject matter, crap like React and MOST of what people derp into their pages with jQuery is the fastest road to fines, civil litigation, and failure to meet contracted requirements... under the US ADA, the UK 2010 ACT, etc, etc...

w3.org/WAI/Policy

See the banking group (international, holds the title to some hundred smaller banks and CU's) that I just spent a month bailing out of some scripttard pissing on their account interface with react.js and jquery-ui in utter and complete ignorance of WCAG minimums or how many users with accessibility needs can't use ANY of the JavaScript bullshit. They gave the incompetent "JavaScript for EVERYTHING" jokers 100K and it's now cost them 4 million to bail them out of the resultant mess!

Now, I'm not saying you can't use JavaScript, but if this is for a real website involving the delivery of content to users, the scripting should ENHANCE an already functioning page, NOT be the means of building the UI and only means of functionality. Remember the mantra:

If you can't build a fully functioning websites without JavaScript FIRST, you likely have zero damned business adding scripting to it!

... and in that way, halfwit bloated garbage like react.js are an epic /FAIL/ at web development!

See the number of developers I know who won't even consider using hashnode for its being scripting reliant -- and how for me to use it I'm overriding tons of the style and scripting using ghostery, stylish and tampermonkey.

As long as you don't change a react components DOM using jQuery, you should be fine. I guess...