the big difference between Acronis and Windows backup are the features they offer. The paid version of Acronis will offer many more features, and flexibility.
However, if I am understanding you correctly niether will acomplish what you want to do.
By that I mean:
Both Image the Hard Drive, or the Partition as it is at that moment in time. To be fair, I am not very familiar with Windows built in backup so I will use Aconis in my examples.
By restoring a full disk Image, Acronis wipes the drive and recreates its partitions and data just as it was the moment it was image.
The same holds true for a partition image, only it wipes and restores just the partition in question.
It will also allow you to brows the imaged contents and restore just a folder, several folder, a single file, or multiple files.
The only was you can recover DELETED files with Acronis, is by restoring said file from a earlier image.
For example, lets say I delete a MP3 and empty the recycle bin. By schedule, Acronis Images my HD.
That file will NOT be included in the image. It was deleted. But, a image from the day before WOULD have that file. I can then access that image, and restore just that 1 file.
The only way to recover deleted files is with software designed for that purpose. Imaging for the purpose of recovering deleted contents will not work reliably, as Acronis backs ups your data.
The deleted DATA itself is remnants left on the HD itself. Data recovery software may see it and often recover it. The more you write to the HD however, the less chance of recovery.
Acronis does not save this DATA, nor does it restore it.