I was curious as I am not familiar with either of these programs. From just looking at their websites, it appears to me that SEMO has probably the more accomplished alumni. The website shows several alums who are EMC or equity members, and many who are working in reputable places.
http://semo.edu/theatreanddance/success-stories.html
Carthage also shows some of their alums and what they are doing . carthage.edu/music-theatre/alumni/ Their alums are not necessarily as recent nor are there many performers.
Of course both schools are just showing a select few of their graduates and what they’re doing, but I assume they’d put the most notable accomplishments on their website.
You may want to compare the two and see which alums are getting the type of work you are hoping to get. Strictly from this very simple, non scientific analysis, SEMO would appear to be the stronger program of the two in my opinion.
I also am a big fan of comparing curriculum and seeing which has the classes you wish to take.