Depends on the circumstances, who the fight is against etc, but if by going down in weight you mean draining the weight then that's obviously going to be harder as you'll be running on empty from the first bell.
Going down is way more difficult., you are melting muscle to get down while you're adding muscle when moving uo. This is for completely fit fighters. For fighters that fluctuate it really depends on how high they go between fights.
But going up means fighting bigger stronger guys. Theres just too many variables to say which is tougher or easier
goiing down in weight if your doing what 99.9 percent of all boxers are doing and draining to get down to your current division.. going further down you obviously would not do because its way to hard for you to get that far down (and if you do then you are hindering yourself)
When I think of this I think of Chris Byrd going down to super middle from heavyweight. I know that's extreme but Byrd got waxed in one round I believe.
Going down never worked for Roy Jones or BJ Penn trying to fight at featherweight. Worked a little for Zab Judah but was a god send for Randy Couture. So it depends on the body type and conditioning of that individual.
Going down in weight, because you lose muscle mass and your training camp is focused more on losing weight than training. It takes a toll on you physically and mentally. Going up in weight is easier because you can be less strict on your diet and probably just lift a little weights, or even cut out some cardio. Plus, guys normally rehydrate anyways. So for them, going up a weight class is as simple as not dehydrating the day before weigh in. And going up in weight, like someone above stated, doesn't always mean you're fighting bigger, stronger men. With that added weight, depending on how it's added, you might actually be on a level playing field. But that's the gray area.