There are a couple of candidates here and they're not the ones you would expect.
Bret was pretty average in this time, while his opponents were not always the best, neither was his work... this was the only period of his career where he genuinely appeared bored a lot of the time.
Diesel wasn't the most valuable either... nor Razor or Shawn... The Kliq in general were going through the motions a lot of late 1995 and early 1996, only Shawn was really making any effort cos he knew he was locked into his deal and wasn't going anywhere. Once Razor and Diesel handed notice, they stopped caring and it showed.
The candidates:-
Owen Hart: Owen was the reigning KOTR during early 1995 and played a part in major storylines all the way through. His tag team with Yokozuna was interesting and effective and he played a crucial role in Bret losing the title the year prior.
Jerry Lawler: During 1995, Jerry was a major part of WWE TV, the force that introduced several new talents to face Bret in their feud. Most notably Hakushi who was, involved in 3 match of the year candidates during that time... it is only poor booking that prevents "The White Angel" being on this list or the winner. But Lawler was arguably one of the better heels of that era and made you believe the hatred of Bret enough that he would be driven to destroy him. Sadly Bret didn't do his best work against said opponents but Jerry more than carried his end.
Savio Vega: The one time Kwang was somewhat of a surprise package during this time, they used the "cinderella push" at King Of The Ring and got in return a very solid midcarder that lasted several years and put on some great matches. He was an interesting partner for Scott Hall and replacemed Waltman as the sidekick of Razor well. Personally I feel they could have gone all the way at KOTR, but they were despereate for a "giant" challenger to Diesel.
The winner however for me is...
Davey Boy Smith: Davey had returned at Summerslam 94 with his newly "long" locks and "won" the Rumble from number 2 before Shawn's "skin the cat" escape...they even played his music... from there it got a bit dicey with the Allied Powers but it was clear after their poor Mania showing that it wasn't going anywhere and once Lex left it freed Davey to begin the most fruitful and best period. Go back and look at his heel turn on Diesel... it was VERY well done... the cutting of the hair, change of attitude all lent themselves to a main event heel being created. He challenged for the title at IYH 4 and 5, against Diesel and Bret respectively and it is one of the great sadnesses that he wasn't given the belt from Diesel to drop to Bret. The reason sadly was his involvment in outside issues, both the Marine fight with Shawn (where he arguably saved his skin along with Kid) and attacking the guy who hit on Diana... both those probably did for Davey as a champion... When Owen was unable to compete he filled in for him, dropping the straps and began the alliance with Jim Cornette that led to he an Owen teaming and his title matches against Shawn the following year. For all his backstage problems, this was Davey's best period in the ring, he not only embraced the heel turn but thrived on it and never went back to being a "good guy" in the WWF unless he was in the UK. His performances were among the best of that time in what was becoming an increasingly diluted talent pool... he didn't get his full due, but what he did here was clearly noticed... in the years that followed he held several titles... in this era, he was definitely the Workhorse rather than "The Bulldog".