Muti-hot encoding vs Label-Encoding
You can think of binary encoding as a compromise between label encoding and one-hot encoding. For distinct categories, label encoding introduces a false linear order that brings a lot of noise into the model (category 1 &lt; category 2 &lt; category 3....) . Binary encoding introduces false additive relationships between the categories (e.g. category 4 + category 1 = category 5 or 100 + 001 = 101) but fewer of them.

Therefore, binary will usually work better than label encoding, however only one-hot encoding will usually preserve the full information in the data. 

Unless your algorithm (or computing power) is limited in the number of categories it can handle, one-hot encoding will be preferred over other encoding schemes. If you are limited, mean encoding is a powerful alternative because it transform a categorical feature into a numeric one (giving you the minimal number of inputs) while preserving the most important information in the data.

[Mean encoding replaces every category with its target mean. The mean encodings need to be constructed carefully on a separate dataset to avoid data leakage. If you want to reduce your input dimensions as much as possible, this can be helpful. Mean encoding can also be helpful as an additional feature and is very popular on Kaggle to squeeze out some extra performance. This is also known as target encoding or likelihood encoding.]