Does a circuit breaker trip depending on voltage or current?
The vast majority of Circuit Breakers are not voltage sensitive, they are current and current/time sensitive.
You can find advanced Circuit Breakers that include undervoltage sensing which are used to protect sensitive equipment from brownouts.
If you like the technical details of why it is Current/Time for most breakers you could read this.

Circuit breakers are becoming more accurate and have active electronic current sensing in the most advanced units. You could read this to get a glimpse, but they are rarely voltage sensitive since the design domain means it's extremely unlikely they would ever be exposed to large changes in voltage within a given design.  

For typical house type breakers the current/time curve is quite extended. 
Read this .....and this is a typical curve:

 

The curve is asymptotic at its rating, so there is no guarantee that a breaker won't ever trip with only its rated current flowing....it'll just usually take a really long time.