With all 1's this is not really possible.Â With a string of random characters it would be a more accurate measurement of real world performance.

Actually, neither would represent real-world performance. Real-world benchmarking would require compilation of various common file formats. Compression targeted towards a specific file format(s) does much better than an algorithm not targeted for them. Therefore, if you were to do tests on pseudo-random or arbitrary data, the best performing compression algorithm would not necessarily be the best performing algorithm on real-world data sets.