There seems to be a lot of differing opinions out there on what is best practice. A lot of people seem to be shying away from the wet sponge due to the thermal stress it imposes on the tip. I have personally always used the brass sponge only, but my Hakko station came with both a "wet" sponge and a brass sponge for cleaning.
What are the differences between the two cleaning devices? How should I decide which one to use given the type of work I do?
Wet sponge: Cheaper, less abrasive.
Brass wool: Removes "debris" better, smaller thermal shock (drop of temperature can be more of an issue than cracks/wear depending on your iron), you don't have to pour water whenever you start soldering.
I personally prefer the brass wool, cleans better, no water pouring, doesnt affect the temperature of the tool so much (although it still drops it a bit).
I didn't know the rationale for brass until a decade ago.
The story goes "wet sponge thermal shock cracks the iron plating eventually, then the tip fails"
I think my tips have lasted much longer since using brass sponge.
It is every bit as good at cleaning the tip as sponge.
I do find I use the hakko tip cleaner button far more with lead-free solders than was needed with tin-lead.
Here's a huge con I've noticed when using brass wool:
When pressing the iron into the brass, it gives/bends. When you pull away, the brass then springs back into place. Why is that bad? Because there may be hot, liquid metal on that brass!
There is a potential hazard to both the project you are working on (think small, unseen shorts), or a safety issue to the face.
I have personally seen my brass wool fling solder into the air and splash onto a PCB of mine. I've stopped using it ever since. Even if I try to be careful, I don't see it worth the risk when the sponge works well enough.
What are the differences between the two cleaning devices? How should I decide which one to use given the type of work I do?
When you have a lot of flux or contaminates, a wet sponge cleans it quickly. The brass sponge is ok, but it seems you do have to train it so it doesn't splatter the solder, but stabbing motions into it seem to not splatter the solder compared to just laying it on top of it and rolling the iron like you do on a wet sponge.
I know some people adopted the rule no-clean : brass sponge and flux and low flux: wet sponge. Their reasoning behind it was the flux accumulates in the brass sponge where it washes away with the wet sponge.
Either way, it doesn't matter to me personally as long as it works.
I didn't consider this an answer, but here's what life taught me so far (as per recommendation from @pipe): I think it's a matter of preference, however, I have to say that I have never, ever, seen a cracked tip due to wet sponge. That doesn't mean that it can't happen. Brass sponge isn't prefect, either, as it may wear out your tip faster due to being more abrasive, but this, too, I haven't seen in practise (but it's also true I I haven't seen more than a few). When in doubt, test for yourself, that's the best way to find out any answer.
Tips cost less than the time wasted on fighting with tools that don't work well. Thermal stress cracks vs abrasion are ultimately completely irrelevant.
Bottom line is that brass is easier, faster, always ready, and cleans the tip better.
I've never seen a tip fail due to reasons that I could confidently blame on a wet sponge or brass. But even if brass conclusively caused a tip to wear down 10x faster I would still use it. Make sure you consider all the costs, including your time and work quality, when making a decision.
