It's important to keep in mind that neither MEME or STREME are performing an exhaustive search over all possible motifs. Such a search would be computationally intractable since the search space is beyond astronomical. Both MEME and STREME begin by making principled initial guess and then refining those. Since they use different algorithms, it's not surprising that MEME and STREME would get somewhat different results. However, most highly significant motifs should look somewhat similar.
In general we recommend STREME over MEME as STREME is much faster and more thorough. The one area where MEME is slightly superior is when you are looking for very short motifs (<= 7 positions).