Honestly, I don't get why people say they have such a hard time with Poppy. My first couple games were rough, but now I do really well. My second ever penta (and first one I can feel proud of -- last one was with Fiora) was with the new Poppy, and I've gotten upwards of 18 kills in a game with her. She's incredibly strong in the right hands, but falls on her face when someone plays her badly (she's like a bruiser Azir -- really high skillcap now).
I don't build her tanky unless I'm supporting, in which case I swap out BC for the 500 HP Eye item. Usually my build is a bunch of damage items, an armor item and either an MR item (usually Maw) or Sterak's (for all AD). Even when built for damage, she still doesn't do much unless you use her kit properly.
Just keep playing her, and you'll get the hang of it. ^^
Oh, and I should mention that I play her in every role but ADC with a good success rate (I think my Poppy winrate is ~50%, and it keeps climbing the more games I play her in). She can be outplayed, but she can also destroy people. I like to invade the enemy jungle at level 2 (after my leash) and get first blood with her, something I usually only do with Eve and Shaco. :P
She's quickly becoming one of my favorite champs.