I think i will go for the landing distance will be exactly the same.
Logic if you land in the same configuration at exactly the same Vref the aircraft will have exactly the same energy whatever the approach gradient is.
Once the wheels are on the deck you have exactly the same amount of drag acting on the aircraft so it will slow the same amount and therefore use the same amount of tarmac.
The only difference between a steep approach and normal is the amount of power or spoiler required to maintain profile.
MJ