Comparison
Addressing one or two points, incl one meant for me...
Mozy's restore has been fine. I never said it wasn't. In forums I have in the past read criticisms of Carbonite, where restores just failed. My gripe with Mozy (version I have) is its failure to back up reliably external HDDs.
I know a couple of people -- seduced by the low cost -- backing up with Carbonite (incl some business data) but I am not aware of either ever having attempted a restore. Anyway, any problems may have been fixed by now.
For larger volumes it is also important that the provider offers the option of sending you an HDD for local restore, rather than leaving you hanging in there for a fortnight.
Yes, Mozy's backup is incremental, so only file changes are backed up. Be aware though, there is a question of recognising an incremental change, but I think that applies to all systems doing incremental backup. For example, I include my Outlook Express mailboxes in the backup. If I have made many changes between backups (or have done a compaction) the software may back the whole file up.
I agree with Narog2000 that incremental backup is important, especially with ADSL.
As regards file name or file path changes, the file with the old name should still there (in the 'deleted' section), giving you the options of restoring it as long as you are within the period before final deletion. Certainly Ahsay permits you to manage that well.
Interestingly, my provider used to use Iron Mountain software (with which I was very satisfied), then switched to Mozy, claiming it was superior. I did not see a significant difference except that the Mozy interface was a bit more versatile; I suspect they struck a better deal. Nothing wrong with that...
FWIW, I am also concerned about privacy in general but reputable firms are unlikely to exploit your data - it is encrypted, after all.