After spending many days at the Indianapolis Children's Museum, I didn't think CMOE had much chance of comparing. To be sure, Cmoe is much smaller and in earlier stages of developing, but it is a legit Children's Museum and several steps beyond the science-lab-in-a-room children's museums you often see in smaller cities.
The building itself is gorgeous and interesting, and Cmoe has done a great job matching up space with exhibits that are interesting and interactive. My children enjoy going there a couple times a month. It's a nice place to spend a few hours.
People have said that the membership/fees are a little high. I feel that the walk-in pricing is very fair and that the membership of $100 is well worth it to have a place to play on a rainy or cold afternoon, or just to check out new exhibits or take advantage of some of the many special events scheduled throughout the year. The programming is well done and they also offer great camps in the summer and throughout the year at breaks.
Whether you're passing through and looking for a place to let kids run off some energy or you're local and want a fun place to come with kids, you should give this a go.