For starters, they're both music as the main genre, and you got 5 of them as a group. The main character starts off clueless about what they're doing, and the least knowledgeable when is comes to singing and dancing. In each of the first couple of episodes, the main character is involved with a situation with each of their team mates, and in the end, they get along together and then get along as a group. Both anime go through the same problem: passing the entrance exam and Ayanagi festival (in Starmyu) and the Dream Fes (in Dream Festival) by performing their songs on stage.
Here
are some differences now:
1. (Starmyu) Main character gets into a famous music school but doesn't really know how everything works, his dream is to become the person who he admires. After seeing a brief performance of him dancing, he wants to do the same. (DreamFes) Main character hands out balloons as his job until a famous celebrity scouts him and offers him to join his company which produces idol groups.
2. (Starmyu) On his first day of school, he meets a friend that goes to the same school and try to pass the audition together. (DreamFes) Main character is scouted alone and doesn't know anyone in the company yet.
3. (Starmyu) Main character's goal is to be part of the Star team, which is a team of 5 created by the Kao Council (you'll see who they are when you watch it) who are the top singing actors. There are 5 members of the Kao Council, so each member makes a star team out of 5. (DreamFes) Main character's goal is to debut in a group
4. (Starmyu) In order to win, they need to get a lot of votes from the audience. (DreamFes) When they're performing, the audience sends cheer cards to their favorite idols, and in the end, they see which idol groups get the most cheers. Whoever has the most wins the Dream festival.
This is my first rec, so I hope I didn't make things too confusing. read more 
