With the numerous online backup services available these days, it can be difficult to choose one for your sensitive file storage. However, if you've already narrowed your search to Backblaze and Carbonite, then you can't go wrong. Both services have been around for years, and have refined their software to be very simple yet powerful. We no longer recommend Crashplan due to it's business-focused nature, and it's complex software.
TL;DR: While we think Carbonite is a great offering, we feel Backblaze is the leader in cloud storage. Their software is extremely well made, and multi-thread backup means your backups happen quickly and efficiently, so you can stop worrying and get back to work.
Backblaze offers unlimited storage, remote sharing and access, courier recovery, along with all the usual cloud backup features. Backblaze is unique in that it's versioning setting allows you to retain deleted and changed files for up to thirty days. Backblaze also allows multi-thread uploading, which means backing up is exponentially faster than other services.
Carbonite is quite similar in offering to Backblaze, but does a few things differently. For one, it's versioning is not time based, but instead is limited to a static number of file versions. Depending on your usage, that can be better or worse. However, Carbonite does not offering the same multi-thread backup as Backblaze, which makes it less appealing if you have a large number of files to upload.