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.