OK:

"Are planetary rings more associated with gas giants or planets with tiny moons?"

IMHO, planetary rings are associated with gas giants, which 'their rings formed' early, during planetary formation when bombardment was high. Other factors have been found, i.e., Enceladus's outgassing via Cassini, but, imho, it may be a minimal additive from what we're seeing as far as the total mass of Saturn's rings (duh). Look up Ciclops on google.

"Because Mars has tiny moons and Mars is a hard target... "

Mars was a hard target, but gas giants reign when it comes to gravity. They were the hard targets. You have to think further back in terms of rings and 'moonlets'/captured asteroids and comets.

Mars' tiny moons are 'captured' asteroids (which will plunge into the planet/Mars in the future. Unlike our moon which is part of our planet and is moving 'away' from us.

Just a thought.