Is a larger hard drive with the same cache, rpm, and bus type faster?

"It depends." All other things being equal, platter density does directly correlate to an increased sequential transfer rate.

However, you need to know what the platter density is. If that 400 GB drive has 2 x 200 GB platters and the 80 GB drive uses 1 short stroked 200 GB platter, then the 80 GB drive would be faster overall (because the average seek time will be smaller).

The extra drive space may end up being useful in some other way over the life of the system though. Unless you're looking at buying thousands of systems were $13/ea is a budget breaker, I'd opt for the larger hard drive immediately. Otherwise if you end up wanting or needing a larger drive, you're looking at not just the expenses of the drives themselves, but of your time spent swapping the drives and imaging the contents.

Personally, I wouldn't install such a small drive in a new system unless there were other considerations coming into play. (e.g. It's an SSD, budget sensitivity, etc.)