"Even worse" is used when:

• Person A is bad, like a "3" on a scale of 1 to 10.
• Person B is worse than A, like a "2" out of 10.

Use "worse at ___" to explain what skill you're measuring.

Who do you think is worse at bowling, me or her?

Use "worse than ___" to explain who you're comparing to:

You're definitely worse than her.

"Even worse" is a pretty negative way to express two people both doing something badly. In the example above, it's OK for the speaker to use this with his friend because he's teasing him. Both the speaker and the listener know that it's a kind of joke (although it might be true).

To explain the same idea but in a more positive way, use "at least":

A: I'm horrible at basketball.

B: At least you're better than me!