First off, this is about the mechanics of the weapons themselves, not melee as a whole.

First topic I want to address is how to make Chainaxes (and by extension Chain Choppas) stand out from Power axes (and electrified choppas) aside from costing less LP and not having the additional penetration. I have not had the opportunity to run with the Chain Choppa (yet), but I gathered that it is basically a noisier choppa blade. Honestly, I think if that's the case, then it's a redundant weapon and aught to be removed. If it has longer reach or something, then fair enough it should stay. On the subject of Chain Axes, I would propose making them as fast as chainswords BUT either restricting them to the Mark of Khorne entirely, or if possible, make them usable by any mark, but only give the swing speed bonus to Khorne devotees, as chainaxes are his holy, favored weapon and Khorne worshippers have the raw strength to use them more swiftly than other marks. No nerf to damage, no need to rebalance MoK (in fact, if this became a thing, my argument that MoK provides negligible benefits for massive downsides would be solved) to compensate. In this way, players who do not have the Manslayer can still be as fearless as their devotion to the Blood God should make them, and the battle-hardened players who have been around long enough to get the Manslayer can fight with that much more ferocity. Seeing a Chaos Marine charging at you with a chain axe should make you cautious. Seeing a Khorne devotee rushing at you with a chain axe should fill you with terror. At a cost of additional LP over the Choppa blade, consider allowing the Choppa Axe to be as fast as the blade, but being an option for those who don't mind the extra cost for the non-penetrating stopping power.

Would it be OP? Not really, considering MoK makes you unhealable except from lifesteal and resupplying, and you die immediately when your health hits 0. If you are not another assault class, you should absolutely feel and be at a disadvantage in melee, and you should never delude yourself into taking one on by yourself. In the case of fighting the chosen of Khorne or a Slugga Boy, you might want two or three buddies with you to take him down because the ballsy motherfucker is about to make his chainaxe intimately acquainted with your face if he gets within reach of you. If you are uncomfortable about going up against this in battle then that's a good thing. You should be, and you should do what you can to avoid getting pitted up against them in melee, rather than relying on the lackluster netcode and the fact that it's an axe to repeat the dbash + m1 bullshit ad nauseum.

Not entirely. To some degree, you get the element of surprise because nobody fucking uses the chainaxe unless they have Manslayer, are masochistic, or are roleplaying, and the damage is substantial, but after the first few kills the shock factor goes away. However, making it as fast as the chainsword when in the hands of a Khorne devotee would be so substantial of a buff that they wouldn't really need to do anything else to make MoK more viable, except maybe an extra 20 health added to the 20 you get already so that you can actually take one or two more shots from a CQC barrel bolter since you are probably taking MoK to go ham with your chainaxe anyway and could use that extra HP to help close the distance when you no longer have the benefit of hard cover.

Slow melee weapons just don't work in a game where TTK is so low for ranged weapons. Animations. It always comes down to the damn animations. Fast weapons means you're "trapped" in your animations for less time.

And we haven't even gotten to the ridiculous LP costs and the fact that it drastically lowers your dps. Oh but dat first hit doh... whatever.

In the case of power weapons, I don't mind the slower swing as much, but currently the problem with axes and mauls is that they are greatly outclassed by the windup speed of swords. It's the heavy attack windup that usually gets me killed, either because dbash is faster and interrupts the windup or because of the way too generous window for fast attacks to interrupt by comparison to the sword or knife. However, if Chaos and Orks get to equalize that by having the MoK and the choppa axe swing as fast as swords for the respective sacrifices in debuffs/LP they make, then it's not as big a problem.

Before anyone says "but what about LSM," LSM gets storm shields that block ALL melee attacks, including dbashes. So you basically get an "i win" button against melee and most forms of ranged.

One sided fix suggestion is one sided.

All melee should have same attack speed - bar PF power attack otherwise RPS system pointless if you cannot even to draw stone in time to counter scirrors.

Id rather see different combinations of damage, speed, impact, resistance and special skills where no weapon clearly shines but one has many choices depending on the play style.

That being said Alb clearly pinpointed the problem, and it's not an easy one to solve: in current combat iteration ranged ttk is very low. This makes slow weapons definitely a bad choice because even you fill the gap with the target you might still be too slow to avoid being crippled with bullets.
For Orks this simply translates in forgetting clubbas and axes, because the swords are so much better. And once you find the burning sword all the other melee weapons are pretty much suboptimal.

To sum up: combat is still too fucked up to let a niche for axes and maces.

I myself prefer what you said but till nimrod system known as RPS is how melee goes by, all faster tier weapons have unfair handicap, they land faster than opponent's slow weapon and RPS simply does not kick in, it's like attacking someone standing still. One may say git gud and initiate attack earlier(only work for 100% if you have precognition) - but there lies problem while this way works on scrubs anyone with decent reaction(I don't say skill cause it not needed) counter slow weapon using damn RPS.

Swords and Axes have same attack speed, Swords have stronger fast attacks, Axes have stronger charge attacks.