Normally one has an annotation file (GTF or GFF) and then supplies that with the -g or -G options. Assuming that it's formatted in a way that cufflinks understands, this should give you more coherent gene IDs.
Perhaps there are simply no significant differences. Realistically, we would need vastly more information to determine how expected this might be (e.g., what was the experimental design, how man samples per-condition, what organism, how many reads aligned and what percentage aligned to genes, ...).
Also, Cufflinks is extremely conservative in calling DE. You might consider the new Ballgown package (http://biorxiv.org/content/early/2014/03/30/003665), by some of the same authors, to see if some statistically significant differences exist in your data under a more liberal (but still mathematically sound) model.