Feud with the Undertaker - Arguably the top best feud in both of their careers. During the Undertaker's match against JBL, Mankind brutally attacked him. Afterwards, Mankind continually attacked him and became the Undertaker's nightmare. Finally during Taker's casket match against Goldust for the IC title at In your House 8: Beware of Dog 1996, Mankind cost him the match by using the mandible claw on him and pulled him in the casket. The two faced at King of the Ring 1996. They then faced in a series of brawls leading to Summerslam 1996. Taker interfered with Mankind's match with HBK out of revenge leading to In Your House: Buried Alive 1996. The Undertaker returned, playing mind games on Mankind which led to Survivor Series 1996. Later, Mankind attacked Taker to hold the World Title and burned his face with a fireball culminating at In Your House 14: Revenge of the Taker 1997 for the WWF championship. Mankind cost Taker yet another match and faced each other at King of the Ring 1998. Ultimately, this led to the feud ending at Hell in a Cell 1998.
Why was this feud the best? Because this was the first time someone at the Undertaker's level challenged him. Mankind clearly wasn't scared of the Undertaker and brutalized him in a series of matches. Why did Mankind attack him? He summed it up perfectly in this promo:
Mick Foley vs. Triple H - The feud between Triple H began around Summerslam in a triple threat with Stone Cold. Triple H beat Cactus Jack brutally and mercilessly. The two then faced each other at the Royal Rumble street fight 2000. The feud ended at No Way Out Hell in a Cell 2000.
What made this feud so emotionally powerful is the transition between Mick Foley to Cactus Jack in a never before seen build up. Triple H however exposes Mick Foley's flaws by saying the real Mick Foley is in real life behind Cactus Jack is a kind-hearted man plagued by guilt over what he does to his opponents. Mick Foley responds by bringing out his Cactus Jack persona, scaring Triple H. Although Cactus Jack lost his matches, he made Triple H cower in fear and still walked out the victor in that respect.
Mick Foley vs. Ric Flair - This was a real life feud transitioning into Kayfabe. In Mick Foley's book, he accused Flair of misusing him in the WCW bookings. Flair responded by calling him a stuntman and dismissed his hardcore injuries. In the WWF, they faced each other in a 2 out of 3 falls at Vengeance and an "I quit" match at Summerslam 2006. The feud continued at TNA in a last man standing match in 2007.
This feud was intense mainly because it was genuine and heated. Both were so focused in ending each other's careers over what happened in the past.
Mick Foley vs. Abyss - Probably the lesser known but most emotionally and brutal feuds that Abyss had with Mick Foley. It started when Abyss saved Mick Foley from Kevin Nash wielding his barbed wire bat at Hard Justice 2009. Fueled by rage, Mick Foley brutally beat Abyss to a pulp and later explained that the feud result from Abyss costing him a match and stealing his barbed wire. The two engaged in a few brawls until they had a heated confrontation leading to Bound for Glory Monster's ball match 2009.
This feud was powerful because it was so full of raw emotion, anger, betrayal, brutality, and drive. According to the story, Abyss as a child was abused by his father but was empowered to grow watching Mick Foley on T.V. He joined the pro-wrestling business taking inspiration from Mick Foley. When he thought Mick Foley was his friend after Mick gave him a flannel shirt, Mick Foley turned heel and quickly betrayed him. Mick Foley wrecked Abyss' self esteem by calling him a cheap copy but Abyss responded by listing his achievements at TNA. Why was the match at Bound for Glory important? Because it was all about Abyss's character growth, proving that he was worthy to be among the hardcore legends. Mick Foley provided a plot twist when he revealed he was only testing Abyss reputation as a hardcore wrestler. This feud conclusively gave Abyss a push.
In summary, this is what separates Mick Foley from other hardcore legends because he had a story to his hardcore matches.