Comparison of data transfer between different bandwidths
In information theory, Shannon's theorem states that the channel capacity is the bandwidth in Hz, multiplied by a two-based logarithm of 1 plus the channel's signal-to-noise ratio. And that the unit of channel capacity is bits per second. Thus if you double the bandwidth, you double the bits per second. But the same amount of information flows when you send twice as long with the original bitrate. So according to Shannon's theorem, the two cases would be the same. 

That said, I don't know what your instructor has been teaching and whether Shannon's theorem is the only one that applies. Maybe there's some another theory that has something to do with the amount of messages you can send in a unit of time and the effect of number of messages to the channel capacity (very important in Ethernet, for example).