I'm looking extension which have functionality to backup both source and database. Also works for both same server FTP and different server. (Clude storage, drop box, etc). And also have facility to check if server have space then only upload backup (on same server) otherwise give error message accordingly. Please suggest good extension.
We've got an extension, which seems to be the thing you need.
Please get more details from here: Magento Cloud BackUp (http://ecommerce.aheadworks.com/magento-extensions/cloud-backup.html)
Check out this Cloud Backup extension https://amasty.com/magento-cloud-backup.html
It has the features you are looking for. It will enable you to:
I'd be careful about extensions that do this (including the built-in one in Magento). They will likely be running inline with Magento, which could cause slowdowns or non-availability of the frontend of your site. The best system here is usually a server-side script - eg. a cron running a 1-line mysql dump, and another zipping your site folder, saving both to a different disk (in case the backup itself causes the disk to be full you won't then cause issues with your actual site).