BackupGuard might be a bit more popular than Duplicator Pro. We know about 1 link to it since March 2021 and only 1 link to Duplicator Pro. We are tracking product recommendations and mentions on various public social media platforms and blogs. They can help you identify which product is more popular and what people think of it.
2, The logical way would be to develop the site on a staging/ dev server then move it to their live site when ready. A few things, again, need to be considered, but, for a straightforward swap, you can use a plugin like Duplicator Pro to 'duplicate' your updated version and overwrite the live site when ready. Source: over 2 years ago
We used to use All in One migration and is a great plugin but I needed an automated solution. We them found backup-guard and been using ever since. Source: about 3 years ago
UpdraftPlus - UpdraftPlus is a WordPress backup plugin.
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