To be honest I wouldn't say difficulty spike for 12->13 was higher than 10->11. I did messed up 13F because of my own stupidity, but floor 11 also put some challenge (goddamn Surtr deleting my Oto-hime with double-strike from normal overdrive).
I would agree with nonsensei on 13 being harder than 14, if it wasn't for friend clearing 13F and failing at 14F. Seems it really depends on person.