Shall I use the Euclidean Distance or the Cosine Similarity to compute the semantic similarity of two words?
First of all, if GloVe gives you normalized unit vectors, then the two calculations are equivalent. In general, I would use the cosine similarity since it removes the effect of document length. For example, a postcard and a full-length book may be about the same topic, but will likely be quite far apart in pure "term frequency" space using the Euclidean distance. They will be right on top of each other in cosine similarity.