All other things being equal, there should be no difference. There's a fixed-size buffer that data gets put into from the hard drive, and it plays that data until it runs out and needs to refill the buffer.
What might actually make a difference is the quality/bitrate of the audio file. A high-quality song would take up more data than a low-quality song, so if it plays a lot of high-quality songs, it'll have to refill the buffer more often. That would increase hard disk usage, which would in turn drain the battery faster.