Asher VS Ludd, and Rodrik VS Gryff.
I like the idea that Ludd is meant as an antagonist for Asher, And Gryff is meant for Rodrik (I know they're not, it's just the way I interpret it). I love how better suited one is for the other, which is why in my alternate Canon with Rodrik, I made sure maimed Gryff survived.
Asher VS Ludd:
I love their rivalry mainly because of their history. Asher was exiled to Essos because Ludd was willing to start a war, because he discovered Asher was in a relationship with his daughter. And now Ludd is the reason Asher came back home. Their interaction is so perfect, things are obviously tense between them, things were tense between Rodrik and Ludd but not on the same level as with Asher. Then there's the interesting dynamic of Ludd being scared of Asher, which makes so much sense. Unlike Rodrik, Asher is an unknown, and he's unlike any Northern Lord Ludd has ever seen. It seems a ruse by Gwyn at first but if you ambush Ludd, you can tell by his voice and expression that he is definitely afraid of Asher, especially when Asher chases Ludd out of the Great Hall.
Rodrik VS Gryff:
I love the rivalry between Rodrik and Gryff, it's just natural, and there's no history between them (that we know of). My favourite Rodrik VS Gryff moment is definitely Rodrik standing up to Gryff in Episode 3. Gryff's anger and attempts at keeping Rodrik down were so brilliant. Gryff has this crazy amount of rage when dealing with Rodrik, Rodrik has an almost equal amount of rage towards Gryff as well. So there's no fear or history between these two, just as natural rivalry, and rage towards each other.
I noticed I said more about Asher and Ludd then Rodrik and Gryff. But don't think it's because I'm playing favourites, it's just that there's no history between Rodrik and Gryff, so I had no history to talk about. I love both of these rivalrys, and I don't think I could pick a favourite.
So, please share your thoughts on these two rivalrys 
Comments
To me, it felt like the total opposite. Gryff is meant for Asher, but Ludd is meant for Rodrik.
How so?
Don't really have a reason, just my own opinion.
Maybe it's due to the fact Rodrik and Ludd were lords of their houses, and Asher and Gryff are pretty much around the same age.
I agree, more or less. Gryff has been antagonizing Rodrik for most of the series, so that alone is enough to make them a good matchup. I don't think Gryff is much of a concern to Asher at all, I feel like Asher completely outclasses Gryff.
I'm pretty sure Gryff and Rodrik have some history, if I remember, he reminds him that they used to call him Cocky Rodrik.
I thought about that, but I wasn't sure if it was worth mentioning, or if it was personal history or Gryff just knew of him.
I agree with this, and I like how one from each pairing could be seen as 'unworthy' as a rival to the other. The rightful Lords of their respective houses VS a savage sell sword exile, or some petulant fourth born.
But Rodrik doesn't? -_-
Because Asher can't kill Ludd by himself....
wat.
Gryff has a prolonged fight with Asher... Asher struggles against Gryff.
^Even one-eyed Gryff
You just read my mind, mate. In Asher's story, Ludd should be killed and Rodrik's, Gryff.