First, I will refrain from asking for a "best" solution, because "best" is in the eye of the beholder. To be clear, I'm not looking for a cloning solution, backup solutions are good enough, although if there is something that can do both I'll give it a look.
To date I've been using Drive Snapshot for backing up Windows. It's very reliable, also not free. But its' interface is amazingly simple. The major advantages of it are that backing up and restoring can be done in a Windows-based environment, and while Windows is running, it can also run in Linux but for restores only. It cant easily back up non-Windows partitions/volumes, unless you do sector by sector. Differential is supported, but no incremental. I'm basically looking to try something new. I also use TeraByte Image for Windows/Linux if I want to full, offline backups/restores. My current strategy is to alternate, doing frequent differentials with DS and occasional fulls with TeraByte.
Right now I'm considering DriveImageXML. It can do full backups, not sure about differentials/incrementals. I've used it a few times but was initially put off that it can sometimes be a bit slow. Info about files contained in the backup are stored in an XML file, but the actual backup contents appear to be contained in raw files that can be interfaced with by other standard software. I like this concept since XML is open and easy to deal with, being able to use multiple tools with a standard format is a big plus.
I also know you can use RoboCopy to back up. And there are multiple solutions for Windows based on Linux's rsync. I haven't researched much beyond that. I really would rather stay away from solutions that use proprietary methods (in which case Drive Snapshot is disqualified, however good it may be). Free is a plus but I dont mind paying if it's good.
So basically, I'm looking for something that has most or all of the following:
1. Preferably free (will pay if necessary), open source is desired but optional
2. Uses standard formats and methods that can be interfaced with multiple tools
3. Can backup/restore various OSes/partition types
4. Supports full, and at least differential or incremental, or both/all 3, I know these abilities may vary depending on what filesystems and partition types it can handle. This is at least preferred for more common filesystems like NTFS, and the Ext* that is most common in Linux.
5. Can do full/differential/incremental on encrypted partitions, I use VeraCrypt for encrypting Windows. I know the volume may need to be mounted for the encryption to remain (or do a sector by sector backup)
6. Can restore NTFS-compressed files in a still-compressed form (something DS cant do, they are always uncompressed again afterwards)
7. Can do hot imaging (i.e. while Windows is running)
I'm not sure about the merits/disadvantages of backup on the basis of files vs sectors, I suppose each has positives/negatives. With a sector by sector backup you must backup/restore both used space as well as free space, I would like to avoid doing this with free space. This is especially important with encrypted volumes, which are raw if unmounted. All my OSes are on an SSD, so there are write-hit considerations. If someone can elaborate their expertise on this bit then I'd be glad to hear it.