Longsword: Length: 106
                    Weight: 1.8
                    Difficulty: 10
                    Speed Rating: 98
                    Thrust Damage: 23 pierce
                    Swing Damage: 36 cut
                    Price: 6660
                    
Katana: Length: 95
             Weight: 1.2
             Difficulty: 9
             Speed Rating: 101
             Thrust Damage: 16 pierce
             Swing Damage: 37 cut
             Price: 9376
Longsword has: 11 more reach, which is in no way negligible; 
                           .6 more weight, which is enough to avoid lots of stuns, whereas the katana can get stunned VERY easily; 
                           1 more difficulty, but they both have such low difficulty already that 99% of viable builds won't be concerned about that; 
                           3 less speed rating, this is the one point that the katana really has over the longsword; 
                           7 more pierce on the thrust, which is quite a nice buff. Thrust on the katana is essentially useless, whereas it can actually deal some damage with the longsword; 
                           1 less cut on the swing, a small negative, imo, but nevertheless it's there;
                           around 2/3 the cost of the katana.
tl;dr: leave katana alone and go grab a longsword.