The way I am looking at it is in the amount of options that you can have in combat with direction mattering, there is more possibilities with squares.

I like how hexes look but it seems to be more for games that involve more strategy and systems that make up for the lack of all directions.

Anyways, that's my opinion related to that part.

What are yours? It does not have to be about combat! Could be anything as long as it's Square vs Hexagonals! And any examples of it being done Great or Horrible?
I think hexes do look nice, but I don't particularly like them when things are moving around a lot or there are other reasons to think about direction (such as combat). It feels kinda unnatural to me and my brain has trouble figuring out distances and paths and such.

That doesn't mean they can't be used effectively, and one of my favorite games ever, Settlers of Catan, has a hexagon board. It also has you build on the corners and edges of the hexes, instead of the middle, so there's only 3 directions from each location. But it looks cool and it makes sense so it works.

This isn't related to gameplay, but hexes in BYOND will require some extra programming. It's not super advanced but would be pretty difficult for a beginner. So unless you think it's crucial for your project to do hexes, I'd stick with the default tile system. That way you can focus more on the actual game elements rather than trying to get the damn map to work...
I totally forgot to reply. I'm such a bad person.

Magicsofa provided a good reply with a similar opinion of how I feel.

Even tho hexagons are preferred to squares because of accurate distance from center to center, it just does not feel correct.

To me, hexagons should be used for very abstract strategy or tactical games. While for tactics, squares provide more interactions if you want there to be more depth.