What is a Fun Puzzle?

Question

What is a Fun Puzzle?

_{I was curious to learn what makes a puzzle Fun so that I could devote my time to only working on Fun Puzzles. With that goal in mind, I set out to make a list of Fun and Not Fun puzzles. I knew this would be a contentious topic with many opinions, so I took an informal poll and below are the results. It turns out, I didn't agree with all of the choices, for example I like Logic puzzles. But I decided not to impose my beliefs, and have passed on the list to the puzzling community.}

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If a puzzle conforms to a special rule, we call it a Fun Puzzle.
Use the survey results below to find the rule.

Fun Puzzles ™	Not Fun Puzzles ™
NO COMPUTERS	KNOWLEDGE
FLAGS	PROOF
LATERAL THINKING	RED HERRING
HUMOR	UNSOLVABLE
FOLDING	OPEN ENDED
PATTERN	TILING
HATS	WEIGHING
REVERSE PUZZLING	CALCULATION PUZZLE
ANAGRAM	LOGIC
VISUAL	STORY
METAPUZZLE	WHAT IS A WORD
MUSIC	CONNECT WALL
NETWORK	PACKING
ENIGMATIC	LANGUAGE
BOXES	AFFIX RIDDLE
CHESS	CRYPTOGRAPHY

And here is a CSV version:

Fun Puzzles™, Not Fun Puzzles™  
NO COMPUTERS, KNOWLEDGE  
FLAGS , PROOF  
LATERAL THINKING , RED HERRING  
HUMOR , UNSOLVABLE  
FOLDING , OPEN ENDED  
PATTERN , TILING  
HATS , WEIGHING  
REVERSE PUZZLING , CALCULATION PUZZLE  
ANAGRAM , LOGIC  
VISUAL, STORY  
METAPUZZLE , WHAT IS A WORD  
MUSIC , CONNECT WALL   
NETWORK , PACKING    
ENIGMATIC , LANGUAGE  
BOXES , AFFIX RIDDLE   
CHESS , CRYPTOGRAPHY 

What is the special rule that determines a Fun Puzzle?

Hint:

If you disagree with the poll results, feel free to swap the columns of any rows for the same answer.

Hint 2:

If it's not clear from Hint 1, this is not a What is a Word puzzle, it is a What is a Fun Puzzle puzzle. Follow the X's and Z's

Hint 3:

The answer to row 1 is ONE. Row 3 is lying to you.

Answer 1

It seems that in the opinion of the OP, a 'Fun Puzzle' is:

ONE FOUND ON THE PUZZLING STACK EXCHANGE!

If we:

Take the letters in each line that are shared by both tags - and ignore those for the line containing 'RED HERRING' (as per the hint), then we end up with the following letter set:

NOE
F
(red herring)
UO
DNO
NT
H
EPUZZLIN
G
S
TA
C
K
ENGA
XE
CH

These can then be:

Split into groups of consecutive letters that can be anagrammed to make the words of the solution:

NEO / FUODN / ON / THE / PUZZLING / STACK / ENGAXECH

i.e. ONE FOUND ON THE PUZZLING STACK EXCHANGE!