Sailing a tug through rough weather at sea is very different than other ships because you're tighed up to something. Everytime the ship gets pushed ahead you feel it being held back. Even though you never get the towingwire out of the water (on long voyages)you feel it. And then there's the occasional frustration when you are releaved from watch, go rest, get back and find out that you have sailed backwards because the wind is pushing you back. (with rigs that is, which are the only tows I did). The other weather thing is that other mariners try to avoid hurricanes and such, on a tug you can't because you're too slow.
They were fine in storms, but you felt like being in a laundry machine..not very different to other types of ships. I think maybe the short length compared to large cargo vessels makes them bounce more, but I would'nt know for sure while I have only sailed suppliers, tugs and a roro across the north sea.