They're health regen weapon upgrading third person shooters published by Sega about fighting robots (and the quirks that come with that). They're different, but have far more of a comparable to eachother than Vanquish is to Doom '16, unless Doom had it so that whenever you went for a melee kill you were completely stripped of mobility and health and had to regenerate your health.
Largely superficial, and on top Binary Domain is a story driven shooter with squad commands. Their pacing and play style is very different. Doom is a much more apt comparison in play design, BD comparison is mostly visual focus. If someone wanted a recommendation for something like BD I'd say Spec Ops over Vanquish unless they specifically wanted a robot motif.