The hardware setup and cabling is exactly the same. Good freeware Windows software is available for both. Tuning in a hellschreiber signal is easier and faster. Hellschreiber is a little slower for sending text. You can chose the text font for sending with hellschreiber.
Weak signals have better quality text with hellschreiber.
I do more rag chewing with PSK31 and more DXing with Hellschreiber. The Hellschreiber frequencies are next to the PSK31 frequencies on most ham bands, so they are easy to mix. As more PSK31 ops discover how nicely the two operating modes compliment each other, we will see more Hellschreiber activity. The very popular Hellschreiber freeware program from IZ8BLY has other experimental hell modes included. Of these, there is another mode besides the traditional Feld Hell mode that hams have found to be useful and are currently using.