its all in personal prefference really. both armours are completly overshadowed by a barrows set in defensive capabilities, so you should only be caring about looks and use. naturally, bandos is good for its strength and prayer, and its ranged defense that excedes barrows, but really, you won't be using ranged defense for much at all. unless you decide you're actually taking that spiritual ranger mission, lol. 3rd age is better overall, so you won't be hit as often, but monster attacks aren't designated all that well, so you really don't know whether its stab slash or crush you need for a certain monster.
visuals: bandos chestplate looks pretty badass, one shoulder though, and interferes with skillcapes similarly to how veracs would. despite that it still looks pretty boss.
3rd age platebody has abdominals carved in it. oh yes, you get to be buff. its also more respected overall because its not seen very often. its also the only white armour that is "trimmed." all the rest are gold trimmed. its a black trim.
bandos tasset: its a skirt >_> and a short one at that. good if you like kilts or want to be a woman, or are female ingame, but being female ruins some of the coolness of the chestplate.
3rd age platelegs: nothing special here either, but they are still cool to have. and if you're anal about skirts, you have a winner right here.
my reccomendation: find someone with full third age or mostly third age and ask for a visual comparison. have him wear the same gear you would, just with 3a instead of bandos.
note: if i were southrend, mr 2 partyhats 500m self value (rich, yet ugly, person

) i'd try to sell one of my lame party hats then buy 3a :p