"lightspeed" is heavily implied to be ludicrously fast. Fast enough that the stars streak out and that going to the other side of the galaxy is a matter of hours. Which incidentally is sort of consistent with the scale of a real galaxy. The comment by the imperial officer is probably just hyperbole to make a point, but still, really damn fast.

While sublight speed is implied to be more in the range of actual lightspeed, going between yavin and the death star only taking a few minutes and flying to another system being feasible at all. It's never really specified how long it takes for them to get to bespin. Judging by the intercutting with luke, at least a couple of days. Although lukes' training is probably heavily time compressed. Of course, they do seem to have a very loose use of the term system, so you never know.

What's really interesting is that luke is never shown to go into hyperspace either when travelling from hoth to dagobah or from dagobah to bespin. Or even from tatooine to dagobah and back to sullust in ROTJ. I guess you could say it was implied. But you do have that rather lengthy scene of him just chatting to r2 while flying.
Were x-wings even supposed to be able to go to hyperspace before the massive hyperspace jump in ROTJ?

It's possible the stellar density is simply very high. You have to remember that here on earth we're in the outer rim of our own galaxy in a rather empty neighbourhood. The density can get as much as 500 times more dense according to estimates. Although this still doesn't explain tatooine which is supposed to be in a similarly remote corner of the galaxy.

In the end, it doesn't really matter. This isn't Star Trek, and you don't have to justify every little thing as long as it works on screen.