Question: Is a bow tie more, less, or equally as formal as a neck tie, or does formality depend on pattern/texture etc?
Answer: Bow ties aren’t really more or less formal than neck ties. They are different.
If you think about it, only the most formal occasions call for bow ties. For black tie or white tie events, the black or white tie in question should always be a bow. These ties are very specific: either satin or grosgrain, in solid black or white. Because of this association with evening and dinner clothes, any color bow tie is particularly at home after dark. It’s a little more fun than the long tie, and so it travels well to parties, openings and the like.
During the day, though, I’d describe it as a more casual choice. It’s certainly more eccentric. You can wear a bow tie in a business context, but only in a business context where it’s appropriate to stand out.
It is important to note that when wearing a bow tie, it may leave much more shirt visible on your chest. For this reason, for the fashion conservative, the bow looks best with a three-button coat, or a waistcoat. Without that higher V, the expanse of shirt may make the outfit look unbalanced.
On the other hand we have found many men pull it off with no jacket at all or even with just a blazer or linen jacket. The whole point of a bow tie is to defy the herd. Most men wear neck ties and the bow tie makes you stand out in a crowd.