A slow weapon does more of its damage up front whereas a faster weapon is forever catching up. This is entirely down to your first hit in melee combat having a 0 second delay (ie. there is none). Draw a graph out if you like and you'll see that a fight has to go on for an infinite amount of time before the actual damage you do with a fast weapon catches up to that done by a slower one. Really obvious example:
Sword1 = 200 damage, 4 second delay (50 dps)
Sword2 = 50 damage, 1 second delay (50 dps)
Second 0 (start of fight)
Sword1 does 200 damage (infinite dps)
Sword2 does 50 damage (infinite dps)
Second 1
Sword1 does 0 damage (200 dps)
Sword2 does 50 damage (100 dps)
Second 2
Sword1 does 0 damage (100 dps)
Sword2 does 50 damage (75 dps)
Second 3
Sword1 does 0 damage (66.7 dps)
Sword2 does 50 damage (66.7 dps)
Second 4
Sword1 does 200 damage (100 dps)
Sword2 does 50 damage (62.5 dps)
Second 5
Sword1 does 0 damage (80 dps)
Sword2 does 50 damage (60 dps)
Second 6
Sword1 does 0 damage (66.7 dps)
Sword2 does 50 damage (58.3 dps)
Second 7
Sword1 does 0 damage (57.1 dps)
Sword2 does 50 damage (57.1 dps)
Second 8
Sword1 does 200 damage (75 dps)
Sword2 does 50 damage (56.3 dps)
You see how the dps for Sword1 goes up and down but never below that of Sword2? It will drop down to the same level (50 dps) and stay there eventually but that will take an infinite amount of time. The quicker the fight is over the bigger the benefit from using Sword1 as well. You will always do just as much damage as Sword2 and in many cases more!
The only time using Sword2 would be a benefit is if your opponent happend to have 201 hit points. It would take 5 seconds to kill them using Sword2 and 8 using Sword1. This is more than balanced by the fact that killing someone with 199 hit points would happen instantaneously with Sword1 and yet take 4 seconds with Sword2. Mathematically it is always better to use Sword1. If you are adding in percentage modifiers to damage or speed then it just emphasises the benefits of Sword1 even more.
Sword1 = 200 damage, 4 second delay (50 dps)
Sword2 = 50 damage, 1 second delay (50 dps)
Second 0 (start of fight)
Sword1 does 200 damage (infinite dps)
Sword2 does 50 damage (infinite dps)
Second 1
Sword1 does 0 damage (200 dps)
Sword2 does 50 damage (100 dps)
Second 2
Sword1 does 0 damage (100 dps)
Sword2 does 50 damage (75 dps)
Second 3
Sword1 does 0 damage (66.7 dps)
Sword2 does 50 damage (66.7 dps)
Second 4
Sword1 does 200 damage (100 dps)
Sword2 does 50 damage (62.5 dps)
Second 5
Sword1 does 0 damage (80 dps)
Sword2 does 50 damage (60 dps)
Second 6
Sword1 does 0 damage (66.7 dps)
Sword2 does 50 damage (58.3 dps)
Second 7
Sword1 does 0 damage (57.1 dps)
Sword2 does 50 damage (57.1 dps)
Second 8
Sword1 does 200 damage (75 dps)
Sword2 does 50 damage (56.3 dps)
You see how the dps for Sword1 goes up and down but never below that of Sword2? It will drop down to the same level (50 dps) and stay there eventually but that will take an infinite amount of time. The quicker the fight is over the bigger the benefit from using Sword1 as well. You will always do just as much damage as Sword2 and in many cases more!
The only time using Sword2 would be a benefit is if your opponent happend to have 201 hit points. It would take 5 seconds to kill them using Sword2 and 8 using Sword1. This is more than balanced by the fact that killing someone with 199 hit points would happen instantaneously with Sword1 and yet take 4 seconds with Sword2. Mathematically it is always better to use Sword1. If you are adding in percentage modifiers to damage or speed then it just emphasises the benefits of Sword1 even more.