Here's a sample clip of a classic Anime called Ninja Senshi Tobikage which was dubbed as "Ninja Robots". Some cover versions can be good depending on the singer. In the case of Ninja Senshi Tobikage, you may want to make a comparison between the original song vs. the cover version.
What's my freaking opinion between the two songs? I really think that the original song called "Love Survivor" beats out "Ninja Robots". Sure the English opening keeps the tune, it has nice lyrics but the problem is the singer's lack of passion combined with a flat voice. The Japanese singer Hit Boy had better vocals than the singer of the English version. The English version needed a more passionate singer than the one they hired.
Then again, I might be having my biases. It sort of happens to me after I've watched Japanese shows that I used to watch dubbed. But after seeing them fan-subbed with the original Japanese audio, I tend to immediately favor the original. In some cases though, some English dubs end up sounding better than the Japanese version and some English covers can sound better than the original Japanese.