I don't know what muscles it works but I do know what you are talking about. I think really your best bet is to stick with weights if you want to work your muscles.
My reasoning is...
The best cardio to be reached is through moving your largest muscles, your legs by walking, biking, running, ellipticalling, stepping, etc. You will get some cardio benefits from the arm bike but I think your best time spent is on a regular cardio machine.
The best weight training to be reached is by using weights (or your own body weight) to work your muscles to failure and targetting various muscle groups. You do get some muscle benefits from cardio but really it is limited. The arm bike really isn't meant as a muscle trainer and it may take your arms to failure but not as effectively as weights.
You can't out-exercise poor eating habits.