Are there any real benefit or difference between hex or square tile maps in strat games?
Wow, could this open up a big old can of forum argument on a wargaming site. 
The short answer is: Yes, there is. There are strong differences between the two styles in how they play because they have a direct effect on movement within the game. This also affects the strategy a player may use.
I’ve played a lot of games over the years of both layout types, digital and physical, and there is definitely a difference in how playing the games feel. But there isn’t a right or wrong to that. Some games work very well on a square grid, others on a hex grid.
Since this is a programming site I’ll also point out that the difference between hex and square grid also affects coding and the tracking of the “spaces” of the game. I personally find a square grid easier to code for as the math to know what space is in what direction is easy.
You typically move by crossing an edge, square tiles give you four directions while hexagons give you six directions. You could even make it circles to get more directions.
They also convey different feelings to the players, a hexagon that got one edge facing the opponent causes the game board to make it very clear when a player is advancing and retreating because there is no side-stepping.
Huge difference is attack sides. With square you only have four sides you can attack on. Of course that means you can only be surrounded by four enemies as well.
You can build a tile map off of any tessellating shape. Why not do something crazy, like triangles or diamonds?