What is the difference in melee weapon speeds in Fallout 4?

This question is more complicated than it appears. Please remember that DPS is largely meaningless in this genre, and not only because mitigation is much spikier than something like an MMO.

If the real question is, "what melee speed is best," well, it depends. For obvious reasons, you want the biggest damage weapon regardless of speed for a sneak attack. For fighting another melee weapon wielder, you almost certainly want a faster weapon than they have, to get as much attacking as possible in between blocking their attacks, and their blocks will mean less per hit.

For everyone else, well, that depends on their armor. The breakpoint for 50% damage reduction is 1:1 damage to DR. For ratios less than that, it ramps sharply up to 50%, and for more than that it slows significantly. (1:20 is ~83% reduction) The upside is, if the average enemy has less DR than your slow weapons, but more or equal than your medium weapons, your slow weapons will do significantly more net damage. If enemy DR is equal to or greater than your slow weapons, it doesn't really matter what you use.

The point is, there's no hard or fast rule to determine melee dps. I wish I could just give you a coefficient for each speed to divide damage by, but it just doesn't work that way.

I did a little bit of testing. Using 2 medium speeds and 1 fast (I don't have any slow) the fast had a speed of 1.1 swings per second, while the medium had 0.76 and 0.6833. So more than likely, slow is less than 0.5 hits per second, fast is more than 1 got per second, and medium is whatever is in between.

In order to know your specific weapon dps, time it for 60 seconds hitting anything, even just the air. Then divide your hits by 60 and multiply the resulting number by your damage. That should be close enough to know the raw dps.

Melee weapon speed will certainly affect your DPS a lot if you can continusly keep hitting the attack button and succesfully hit an opponent every time. Just try it out with a knife compared to a bat. However I'm not sure exactly how much, I'd say maybe 50% difference from just the feel of it. (Needs more testing)

However in reality you won't be hitting enemies constantly with a mellee weapon. If you go pure mellee you will have to block or time your attacks so you avoid being blocked. In addition a slow weapon might often leave your enemy with 10% health, forcing you to do a second swing just to deal the last 10%. So faster weapons will be more consistant in the number of hits required and will waste less damage. In addition if you have a chance to stun enemies on hit this will be more effective with more hits which you get from fast weapons. If you are just using mellee weapons for dealing high damage in stealth then I'd say it's better to use slower weapons but only because they usually have more damage. If you find a faster weapon with more damage that is obviously better. The DPS just won't matter that much in this case.

Regarding strength bonus to mellee damage this could affect the DPS if the bonus was additive. For example if you got +10 damage for every point in strentgh. However it looks like the effect is +% damage from strength (again this would require some testing). So I don't believe that this would affect your DPS.