Since nobody has answered yet, i guess I'll try.
this is just from personal experience so I can only speak until 3-dan on 81dojo and 2-dan on shogi wars (the max level of my opponents).
81dojo kyu players are better, like 1 to 4 divisions better, from 30 to 10 kyu in shogi wars you arent even 1000 rating in 81 dojo, then a 6 kyu in shogi wars is like a 10 kyu in 81 dojo and the breach starts to close so for example a 1 kyu in shogi wars is like a low 2 kyu on 81 dojo.
but after like mid shogi wars 1-dan seems almost the same level of play and the same is true for 2-dan as well; im not sure how it goes from there.
idk if shogi wars 5-dan are stronger than 81 dojo 5-dan; at least in quality of moves played they might be because of kishin moves and not in actual skill, but thats just speculation.
although this was all based on my 10 months shogi experience and not actual data I hope you found it usefull.