Until we see a video of this actually happening on who wins, the points brought up here could go either way.
The brown bear will win 100 out of 100 matches. Brown bears (or any bears for that matter) are very vicious. There is a reason why veterans would say "Don't bring a knife to a bear fight. Shoot them with half a dozen buckshots from far away instead." The full plate armour means nothing when the brown bear not only has monstrous strength (one slap from their paws has enough strength to break your neck if it hits your helm) it is also much more agile than a guy in full plate armour. So before you can even swing a sword, you'd have already been beaten twice or thrice. Each one is as heavy as being hit by a war maul. Now if the knight wields bear arms while the brown bear wields a longsword, the outcome may not be so certain.
I think the knight, if he uses his monkey brain and plans out the confrontation in all aspects first. Getting an element of surprise and having an advantage in ground they are fighting in, higher ground or cover to keep your distance. The long sword should be replaced a long range weapon if you really want to do this sensibly. Basically acting like a thoughtful hunter rather than a meat head brute forcing a head on confrontation. But that wasn’t the hypothetical that was asked. Man vs beast isn’t usually in a mans favor unless you’re talking long distance running. Humans have a great cooling system that lets them out run a horse on hot days. But a bear has a faster sprint, a man can out run in distance running assuming he doesn’t get caught in the first few hundred yards. Then when the beast is exhausted go in for the kill. Probably best to ditch any armor for this strategy.
hmm? knight can win~ condition~ weapon spear~ meh since limited to Long Sword ok not knight who want honor thing but on level real soldier who have fight on crusades life and death battle or something like that~ there clear discrepancy between those who have life death experience battle and those who not~ armor can be hindrance and there high chance to cast off~ anyway on battlefield weapon such as spear is better than sword for melee fight~ sword is secondary weapon~ hence this scenario is really weird~ hmm too much battle on city/castle area? this cat have different view imo da aspect is death and live battle, experience plus weapon~ amphitheater on rome, human vs beast~