Currently, I am facing a choice of encoding some information either in a binary vector or a normalized (Gaussian) floating point vector of the same length. For instance it could be in the format $[ 1, 0, 1]$ or $[0.998, 0, 0.002]$ (both these may represent the same data point depending on the encoding I use). If I use the former, I know that I am doomed to use the Jaccard similarity for measuring similarity, and for the latter, I can use efficient and effective methods like a kernel function. However, the binary encoding is less costly at the encoding step than the Gaussian vectors.
My question is whether there's an added advantage (disregarding the obvious setback on computing the floating point numbers) in using the latter over the former, perhaps in terms of accuracy and performance?