Bottom-line: Beserker no longer adds to gameplay. The two top tier weapons which shouldn't have any difference in use except in weight, power per hit, and playstyle, are now worse than your second tier fireaxe, and first tier machete and knife.
The katana can no longer storm crowds of enemies with holding the mouse button and aiming correctly. It has become a second tier because it only has power like the fireaxe. The speed, which made it a dooming weapon, like a third tier, is missing.
The chainsaw is no longer good at attacking any kind of enemy. The average fleshpound takes almost twice the exposure it used to before death. All low level enemies run around and make for annoying delay and wasting precious time and ammo. It has become barely a second and a half tier, it's almost a useless weapon except at lower levels.
What used to be a slower choice that had more power for its speed, is now just a katana, with useless power. You hold the button down and nothing really happens.
In my opinion, the solution isn't simple if you want correct balance. Because enemies can storm you easily, the katana should still have the option to do the hold and swing method. Only, when the button is held, rather than being tapped once every second, the swings gradually get weaker and/or slower. Making spam impossible and for skill to be required.
The same can be done to the chainsaw's powerful alternate fire, only each swing gets much slower and much weaker when held because of added weight. But the chainsaw has the advantage of being stronger in spam procedure, due to no extra stamina needed for holding down the gears in regular attack mode.
Thus the chainsaw is for the man who is going to focus on the big enemies, but needs his spam to take out all the small enemies with ease. He can also stand doorway and keep guard, generally at higher levels, thus ending an extra path made by a broken door.
The katana is the crowd control man, and can also handle larger enemies. Only due to the third tier rank of the katana, more skill is required to be an all around ninja. He is useful in eating up quickly all the enemies because of the extra length due to using a sword and the extra speed given due to it being A ****ING KATANA.
The other more simple solution would to just given the chainsaw back its power, as I can and have seen many users use the katana with ample skill and prowess to last in a situation. Scrake still gets owned pretty badly, fleshpound is easy to take out. Only, your beserker isn't really needed now at hard mode, only suicidal and such.