There are advantages and disadvantages to both.
New Installation
Pros
- You get to start over. Any mistakes you made or anything you didn’t do right you can do over. I know from experience that every time I create a website I become better at it.
- Fresh start. Any plugins that leave stuff, unused media, customized theme, you get to restart.
Cons
- It involves lots of work. It is no quick process to create a completely new website.
- You need to transfer all your content and media over.
Repairing Old Installation
Pros
- You do not need to transfer content over. It is all on your website.
- All the major setup and installation is done already.
Cons
- Redoing a website over a website can cause a messy, slow website. If you don’t properly clean up your website then it will affect performance.
- You need to figure out what is up with your website. You may end up basically starting over again because you can’t understand what is up with themes and plugins.
Conclusion
To sum that all up really quickly, they both have there advantages and disadvantages. Although, I would say, if you have the time then completely restart your website. Especially restart your website if you are changing most of it (theme, some plugins, SEO, etc.).
If you don’t have time to redo your website then I would suggest a hybrid method. Keep old website, but delete almost everything on your website (theme, and plugins. Not content). This will almost serve the same affect as a new install but will involve less time.