Basically DEFLATE beats GZip because its faster at decompressing. Choosing a compression scheme should be about balancing the transmission time with the decompression time, compression time is the least important aspect of the problem since caching can help mitigate that problem.
Statements like "This algorithm compresses better than gzip/deflate, at the expense of slower compression. Decompression is much faster than compression." mean nothing because its not telling you if the decompression time on a mobile device is worse than if you had sent it without compression. Plus I'd be surprised if there was any algorithm that was slower to decompress than it is to compress.