I am trying to migrate my existing wordpress site to a new server. (I am not able to do the migration with a plugin as it complains about some column format.)

I have downloaded the public_html folder from the existing site.
I have a fresh installation of wordpress installed on the new site.

In the manual migration instructions it states:

It's time to upload the files to your new hosting account. You can use FTP to transfer them.
To install WordPress, you need to navigate to your public_html folder or its subfolder where you want to install it.
Upload the files from your computer to the newly designated location.

At this stage can I safely replace the new website’s public_html folder with the original site’s public_html folder? Or might there be a hosting / wordpress / version mismatch of some type?