From my perspective; both are based on Linux, both are companies based in Taiwan. The QNAP OS (Qnap Turbo Station) is intuitive for Apple Mac users, The Synology OS (Disk Station Manager) is intuitive for Windows users.
Qnap is more a build it yourself solution that lets you select from many hardware options and sticks to EXT4, everything is an add-on. It supports more traditional RAID levels and can appear bare bones. RAID drives need to be identical in size.
Synology is more a complete solution out of the box preconfigured hardware with fewer options, with access to BTRFS out of the box. RAID drives can be different sizes and leverage SHR (Synology Hybrid RAID) 1 and 2. So in that way its closer to having Drobo like features.