You give up some benefits by not learning it, since beeing more versaitile always is a good thing, but blue isn't exactly better than trinity+er+ie.
Blue Ez is better for poke in a siege, as you don't need to AA anything for mana, and he has the nasty slow. His poke also kicks in earlyer, as manamune+iceborn costs way less gold than trinity+er.
He also is better dueling other adc once he has iceborn due to the armor(till they get LW), and he's generally the savest carry with that built.
However, blue ez lacks some raw damage. If he ever falls behind vs a decent frontline, he will do rather poorly, as he lacks the damage to really shred through tanks and his main damage can be bodyblocked by them.
Blue EZ mostly is for gripoing mid with a 1-2 item powerspike and just pokeing/kiteing, and his lategame vs squishy setups also is good.
Trinity EZ has a better 1 item powerspike. trinity simply is far superior to iceborn+tear in terms of damage, and the mobillity is nice. And later on, a crit built offers stronger 1v1(speaking about 5-6items) and superior damage, especially vs tanky opponents, but therefor he is more squishy and has a worse midgame and he lacks the slow.
For soloQ, i'd suggest keeping the trinity built. The blue built needs more teamwork to work well (starting in champ select with a fitting comp) and you have to work around his powerspikes. In most progames that he wins, he is use together with other midgame spikeing poke champs, siegeing down turrets as soon a the iceborn is finished,
