In general, I believe that the better construct would not bypass Damage Reduction. You would need to have a construct with a particularly made weapon, such as adamantine, magic, or whatever is needed to bypass the given DR. (it should be clear that unless otherwise specified, a contruct's natural weapon is made out of the same basic material as its name, or requisite materials for construction suggest)
Note that the natural armor value of each construct is dependent on its' material, and from a cursory inspection of the bestiaries for 'animated object' and the various golems, it appears that most constructs either have DR or hardness. DR and hardness are similar, where both subtract up to a fixed quantity from the damage dealt. The difference lays in which rules apply. DR is fairly well covered in many places, while hardness is maybe a little more difficult to research. In general, hardness less than 20 is overcome by adamantine weapons, but it does not fall under many of the rules that govern bypassing DR.
As far as intuition, I can see how that interpretation seems valid, but consider this:: A level 7 barbarian has DR 1/-. Unless we want to claim that the barbarian has flesh that is stronger than any metal in the game, we cannot let constructs bypass other construct DR unless they also bypass the DR of the barbarian. Better analogies may exist.
EDIT: Sources --
Ultimate Magic : Building and Modifying Constructs
Bestiary 1 & 2 : Animated Object and the listings for Golems
Core Rulebook : Additional Rules
No, hardness does not bypass damage reduction. The construct fight is likely to be long and loud.
No they dont bypass DR unless the specific construct says so. Some things which make sense in real life are not rules for various reasons.