WARNING: This post contains a lot of opinions and babbling.
The parries in Twilight Princess are just a couple Hidden skills. Helm Splitter and back slice (and ending blow if you count magtails/wallmasters/ganon). Only problem I had with those is that they felt a little clunky when executing them. Mainly because you had to do something else before doing those moves. Helm Splitter requiring the Shield attack, and the Back Slice requiring a jump first.
The back slice could be fixed by making it so tapping does jumps, and holdng it down makes you roll. There are a few enemies that I prefer to do short hops around in order to kill them instead of the back slice, so a few playthroughs I ended up purposely not getting all the hidden skills because of the back slice. Mainly because Back Slice leaves you open for attack for such a long time, whereas short hops are a much safer option.
As for the Helm Splitter, maybe pressing the shield attack and jump at the same time would trigger that for whenever you want to do it on an enemy that doesn't require you to shield attack?
The other problem I have with these is that they aren't so much as counter-attacks as much as more ways to attack your enemy. Since you can just wail on enemies because of these Hidden skills, you don't have to wait for the right moment like in Wind Waker.
Mortal draw is my favorite of the Hidden skills though. Makes me feel like a badass everytime.
Ending Blow is too clunky too pull off when you are being swarmed, I would only use this if there's only 1-3 enemies around (unless there's a lizardfos around, they are too fast to let you get up or let you get away for that).
Jump Strike overall needs to be faster. I only use it as an opener on un-suspecting enemies, or enemies running at me from a distance. Getting hit mid-jump or when charging is annoying.
Overall, I'd say Twilight Princess and Wind Waker are just two different swordplay styles.
As for Wind Waker there's a few different variations on the sword combos that you can do other than the standard horizontal, vertical, and thrust, and all the attacks are much faster (except the slowest attack where you spin around and then slice verticaly in front of you, which I've never seen anyone else use on purpose).
Twilight Princess is a bit slower, lacks the silly sword combos that seemingly only Wind Waker had (that no one ever uses sadly, probably why they removed it TP). Perhaps you like TP's swordplay because it feels like each hit has more impact than Wind Waker? Which would make sense, since There's a gigantic red slash when you hit enemies, and I think the time that the screen stays frozen upon hitting an enemy stays longer in TP than it does in WW (probably because you usually don't fight as many mobs. TP has a tendency for you to focus on 1-3 powerful mobs instead of hordes of weak enemies).
Even though it doesn't have the combos, it instead adds something more people will notice, by adding a shield bash, mortal draw, jump strike, and ending blow. Not counting Great Spin because it's just a power up, and it requires you to be full strength as well, and most people I know have a hard time staying at full health.
When it comes to what I want to use to beat up enemies:
Wind Waker for using it's fast and smooth swordplay, and misc weapons that can be used on all enemies, just some enemies are more resistant/weak to certain weapons (You weren't forced to use specific items for enemies in other words, which is one of my problems with TP).
Twilight Princess for Mortal blow, Wolf form, and the Bows (They maybe clunkier, but somehow they feel so much better when they hit [they do 1 shot a lot of things as well]...... And Infinite arrows glitch)
Funny thing is, Wind Waker used to be my most hated Zelda game (At the time it came out I was against things from going serious to being cartoony, I've gotten more open minded since then. Man I feel old.). Now Wind Waker is my favorite Zelda game to replay. Twilight Princess I've always liked. The dark world + wolf thing kind of got me hooked right away because of the other video games + other media people had me play/watch around that time (I can't remember what I played/watched that would make me like either thing though).
Now as for the parrys/hidden skills being added to the links. I think Toon Link should get the 2 parrys from his game to should how quick+nimble he is. Link should get the shield attack or jump attack to show how defensive and/or strong he is.