Hive is an abstract puzzle game, and if you hate the very idea of Chess, Go, or anything of the sort, it won't be for you. However, if you're looking for a deeply engaging competitive puzzle, it's nothing short of fantastic.
Comparisons between Hive and Chess/Go are inevitable, as it takes elements from both. As in Go, the game begins with a blank slate, and pieces are continuously added to the 'board'. And as in Chess, each piece can be moved in a particular, constrained way, with the objective being to capture a specific, and particularly slow, piece of your opponent's. However, in both of these venerable ancestors, the lack of these things - movement of stones in Go, and the inability to add new material to the board in Chess - are core elements, so by combining the two Hive introduces a completely different puzzle. The bughouse variants of chess are, perhaps appropriately, probably the closest equivalents.
This new puzzle holds up admirably. I have generally found it requires a similar mindset to chess - visualising combinations, looking out for tactical opportunities, and evaluating the value of 'trades' - but adding a the ability to add a new piece (which will happen a lot) will often completely change the nature of the game, so both players need to be aware of the possibility at all times. The game also uses its physicality in interesting, intuitive, and very satisfying ways. Pieces can crawl on top of the hive to disable those underneath them, and pieces can only move through gaps that the tiles can phyiscally slide through.
Aside from actual gameplay, a very important difference between Hive and its ancient ancestors is simply that Hive is new. Chess and Go come with the baggage of millenia, and of mass popularity - opening theories, ranking systems, and more expert writings than anyone could ever read. Comparatively, Hive feels like a breath of fresh air, an exploratory game where every decision you make may be a genuinely new one, where you're happy to try something weird just to see what happens, and in which new players can meet on an even playing field. You'd be hard pressed to find a Hive prodigy who's been playing since before they could read.