The black tie with the charcoal suit and white shirt is just a very colorless, severe look which doesn't typically appeal to me. To me, the look amounts to almost a caricature, bringing to mind Joliet Jake and Elwood Blues (although, in fairness, their suits were black, not simply dark grey, their skinny black ties weren't Grenadine, and you didn't mention anything about sunglasses), or some 20-something fellow trying to look hip or edgy. As for the navy tie, if it's dark enough to look black to most people under typical lighting, it's got all the disadvantages of the black tie.
Please bear in mind, these are just general observations. Many exceptions do exist. Nor is there anything inherently bad about navy or black grenadine neckties. In fact, I'd maintain that solid burgundy, solid navy, and solid black, should probably form the core of most men's assortment of either silk knit or grenadine neckties.