I've mained Ezreal since mid S4, and while I've always been unranked and kinda blow at the game, I've been in games against all plats in a Silver ranked team last season(dat matchmaking tho) where I stomped, if that counts for anything. So, here's my insight.
I like Blue build. It's pretty fun and I dive towers 20x more than I really should, so the armor helps. That being said, Blue build is pointless unless you're pretty bad at Ezreal, you've got a rough team comp to go against, or your team is hella good and can play to your blue build. Even if you still want tear, TF ER Ezreal not only does more damage with Q's unless you happen to hit one while triforce is still on cooldown, in which case IBG does ~13 whopping extra damage as opposed to the 70 or so extra on TF. It also snowballs much harder, gets CDR while still building damage, and ENCOURAGES AUTOATTACKING, which most Ezreal players seem to avoid like the plague for some reason or another.
Overall, you're sacrificing poke, snowball, and all in potential for a slow and some armor. But the slow isn't needed on Ezreal, since he's the safest ADC, and I've honestly found phage MS and Zeal MS from triforce more effective at kiting enemies than a slow, because in most situations, an enemy's movespeed isn't why Ezreal died, it's their gapcloser and lockdown. That, and the ensuing followup. But with IBG, you'd only be increasing relative speed towards the people who you've slowed, not the rest of their team. Phage + Zeal speed + Merc Scimitar will pretty much get you out of anything, there's really no need for the slow. Most people who will have more MS than your triforce speed after they've jumped on you have likely already killed you, and would likely do the same regardless of Iceborn. I also just really like where Ezreal's AS sits with a properly stacked passive and a TF, personally. Not so low you feel clunky, but not so high you're wasting it stats because you're tossing Qs.
Another thing I see people doing is immediately upgrading to Manamune. I prefer to keep it as a tear and buy a sheen for the poke and farm, then finish my TF item. Once you've got tear, if you've got it, you need it to hit Muramana ASAP. While it might sound good on paper, "Oh, I can proc TWO tear stacks if I Q something and it lands!" you lose the one mana per 8 seconds passive, which is 4 mana(1 stack) every 32 seconds. 2 stacks a minute, at the 15-20 minutes you'll have tear for, is 120-160 mana out of the 750 needed, so as long as you're casting spells at a good rate, you'll actually stack it much faster without upgrading.
Possibly the worst, though, is when people build tear every game. Some games it's just ridiculous to buy, either because you're snowballing so hard it's better to just buy damage, or because you'll definitely need the combat stat edge when everyone gets level 6. I still have no idea why people insist on buying a tear against other Ezreals, knowing full right well that if he buys a sheen, they're going to get rolled so hard they won't have any impact on the game.
Last, but not least, Blue build kind of encourages new players to say "Oh, I've got armor and MR from merc scimitar, I'm beefy and safe!", then proceed to overextend, overestimating the value of their safety. IBG's safety gap between Triforce can easily be closed with proper positioning and awareness of the Triforce user, and it's honestly just easier to make picks with TF Ezreal. If you're in a team where you need IBG's slow to make a pick, chances are you're in a bad team comp.
TL;DR, Blue build has less damage and since it's the flavor of the week people don't auto as much as they should be, either, resulting in even less damage, and generally get fully stacked way too late.
Added note: If you go for TF ER, even if you start lagging behind, you'll be decently relevant. If you go for blue build and ANYTHING goes wrong, chances are wet noodles are going to start getting together and making fun of how weak you hit.
That disorganized ramble aside, I'm not done with it on my team because it's still decent enough to play. But if you REALLY wanna build IBG and help your team, the optimal build path is definitely armor quints & seals, IBG, Frozen Heart, Deadman's, double thornmail. AOE slow's hella cash, 100% legit, Ezreal top new meta.