Hello,
I backup some drives with HDD Raw Copy tool. However, I can't get speed better than 50MB/s, even with modern, SATA3 drives. Is there any way to increase copying speed? Or maybe some another tool (must copy sector-by-sector)?

Are both drives connected directly to the motherboard, or to a USB3 port with a USB3 external enclosure / adaptator ? What speed (RPM) and capacity are they ? If the slowest drive (source or destination) is a 2.5 5400rpm 160GB HDD, then it's pretty normal, it can't copy at a much higher rate than that. If both drives are 1TB+, that's not normal indeed (even a 5400RPM 1TB HDD can reach a throughput of about 100MB/s), but it's unlikely that the software is the culprit (I don't know that specific tool, but if it's designed for raw copy it should use the maximum transfer speed available). Benchmark each HDD with something like HDTune. Verify that no other process is accessing those HDDs in background during the transfer (indexing, defragmentation, shadow copy...).

Aren't those two likely to be somewhat slower, considering that they're designed to deal with problematic storage units ? Or is, for instance, ddrescue just as fast as the basic dd command with the same source / destination drives on the same machine ?

What would be the specific reason for that ?

I got the same speed 49 MB/s with Win 10 + 2x WD Red EFRX + 2x external eSata-III enclosures with eSata cables.
When connected these enclosures (Fantec 6G) with USB 3.0 cables HDD Raw Copy speed dropped to 42 MB/s.
Just to compare file recovery software (PhotoRec, EaseUS Data Recovery Wizard) was reading 120 MB/s both scanning 3 TB under 8 hours (eSata), while my EliteBook has older Sata-II (3 Gb/s) board. HDD Raw Copy Tool goes for 20 hours.