One of the problems that must be solved one a larger project is that you want to put your code in many small files,like put each class in it's own file (similar to how you would do it in other languages) , because you do not want to import each small file you need a tool that will merge them in one big file and for production maybe also minify it, also you will want source maps to be generated so you can debug your code. So to solve this problem in larger projects you need a tool, I am not familiar with all tools that exists to solve this, the project I am working one uses gulp (I did not made the choice so I did not done the research why gulp was the best solution then, and now something else may be better)
Other problem in big projects with jQuery is caused by the fact that data and UI are combined(what I mean is I often see data set as attributes on UI elements ,hidden fields with data in it), this can be solved if you use jQuerry better though, if your UI is not very dynamic I would continue generating it in server side but if you want something like an infinite scrolling list, or a very huge list then it is more smouth to implement it on client side and implement some tricks to have it work efficient(react would work better in this case then jquery and maybe you can find a good component that you can use),React is used for UI.
Some people compare angular1 with react, angular is a full framework it contains a lot more, like translations support, ajax support,routing , If you want my opinion here it is, angular templates vs react : reactis pure JS , you can use JSX and you should use it but have a look at the generated .js files, when I started I did not use jsx so I can learn better what actually happens.
Angular templates feel to me as magic, there are no generated js files, the templates are compiled at runtime, I am sure eval is used too, in case of errors if you are lucky you get a printed stacktrace (not a real one)) if there are other errors you get a generic error message with a link to a generic solution and if you are not lucky nothing happens, no errors, no application loading. If you need to do something more complex you will have to get your hands dirty and have a look under the hood and maybe use the $compile. Also react can be used in existing jQuery projects, I have worked on such a project where we migrated some components to react and keep the rest using jQuery.
If you like languages like C#, AS3,Java then I suggest trying TypeScript , TS works great with React.
P.S. I am not a person that tries tools, frameworks and the latest shiny thing, I am working on web projects that were already started, so I seen what problems and what solutions we faced, until some of the solutions get standardized then there will be more alternatives, you will have to identify the problem in yourproject, then try to find the simplest solution for it and also try to not bet on the technology that is at the end of life(it is not easy)
Other problem in big projects with jQuery is caused by the fact that data and UI are combined(what I mean is I often see data set as attributes on UI elements ,hidden fields with data in it), this can be solved if you use jQuerry better though, if your UI is not very dynamic I would continue generating it in server side but if you want something like an infinite scrolling list, or a very huge list then it is more smouth to implement it on client side and implement some tricks to have it work efficient(react would work better in this case then jquery and maybe you can find a good component that you can use),React is used for UI.
Some people compare angular1 with react, angular is a full framework it contains a lot more, like translations support, ajax support,routing , If you want my opinion here it is, angular templates vs react : reactis pure JS , you can use JSX and you should use it but have a look at the generated .js files, when I started I did not use jsx so I can learn better what actually happens. Angular templates feel to me as magic, there are no generated js files, the templates are compiled at runtime, I am sure eval is used too, in case of errors if you are lucky you get a printed stacktrace (not a real one)) if there are other errors you get a generic error message with a link to a generic solution and if you are not lucky nothing happens, no errors, no application loading. If you need to do something more complex you will have to get your hands dirty and have a look under the hood and maybe use the $compile. Also react can be used in existing jQuery projects, I have worked on such a project where we migrated some components to react and keep the rest using jQuery. If you like languages like C#, AS3,Java then I suggest trying TypeScript , TS works great with React. P.S. I am not a person that tries tools, frameworks and the latest shiny thing, I am working on web projects that were already started, so I seen what problems and what solutions we faced, until some of the solutions get standardized then there will be more alternatives, you will have to identify the problem in yourproject, then try to find the simplest solution for it and also try to not bet on the technology that is at the end of life(it is not easy)