I feel that weapon choice should matter, and I would like a bit more differentiation between them. There are many ways this has been done (such as AD&D's damage vs size, 3E's crit range, or 4E's attack modifier), and new ways this could have been done (fighting styles, feats, class/racial abilities, even backgrounds). 5E has (currently) chosen to ignore this, trying to hit the difference between those who like 13th age style and those who desire more realism (and appealing to neither, IME).
Fortunately, it's not hard to houserule for either style. I've added several weapons to my game, and I've added a rule from the playtest that makes non-versatile weapons more useful (small characters MUST use versatile weapons in two hands, but gain the benefit as normal). Admittedly, some weapons are redundant (such as the glaive and halberd are in the PHB), and I've combined those to save space (such as the scimitar/sabre/cutlass, longsword/broadsword/bastard sword, and claymore/greatsword).