I killed Garl at the Raiders camp and looted his metal armor. It weighs a lot more than my leather armor, but I figured it must be worth it. Much to my surprise when I put it on instead, my armor rating *reduced* by 5 points. Is this right?

Check your agility ...has that stat been changed in any way?

armor is little more complicated..
you have armor rating - it value reduce enemy chance to hit, in leather you are more agile so it is easier to jump away from rocket, in heavy metal you are like medieval knight, so you move more slowly, instead of dodging, you take hit which is blocked by this armor
then you have damage resistance - this percentage is substracted from damage done to you
and finaly there is damage treshold - this damage is substracted from damage of shot that hits you
If i remember it right:
you have leater armor and your final AR is lets say 25, your enemy have 75% to hit you with 10mm pistol ( ? 5-12 ? ) and you have DT/DR 2/20% (just for educational purposes, i am lazy to find real values)
so in the end your enemy have 50% chance of hitting you (75 ChtH- 25 AR), if he hits you, lets say for 10HP, DT is substracted, semifinal damage is 8 (10 dmg - 2 DT) final damage is around 6.4 (8 dmg- 20%) rounded to 6
in ten shots it means 30 dmg to you
in heavy metal armor (DT/DR lets say 6/40%) its 70% chance to hit (75 ChtH - 5 AR) with same dmg of 10 you will get in semifinal 4 dmg (10dmg - 6DT) and in final 2 dmg(4dmg - 40% = 1.6 rounded mathematicaly to 2, maybe game round always down)
in ten shots it means 14 dmg to you
conclusion ? maybe the will hit you more often but they will need more firepower :)
PS hope i am right and it is as I say and not other way ( DR first then substract DT), in this case my apologies ;)

My agility stat remains the same at 8. Also, no extra AP points, if that was what you were thinking... My AC rating dropped from 23 to 18 when putting on the metal armor. Is 'Moonfear's explanation' (from what I can understand) saying that in the end I'm actually better off by wearing the metal armor? I just want to know - which armor is better...? Thanks.

depends if you want to rely on dogding hits, or taking (alot) less damage, generally id prefer the metal armor but in some situations the leather armor may be more useful. It all depends on your decisions.