That "past" you're talking about is 2006-2010. And what is it that you find cute? I mean, art styles change over time, so if you define a particular art style as "cute", then you'd be right since that art style has become less frequent.
>I feel like the art and characters were cuter in the past
The problem with that statement is that you judge characters' cuteness subjectively and try to place them in a time frame. Cuteness isn't history just like beauty isn't (some people used to date greek sculptures based on their beauty rather than on their style which is, of course, bullshit). Besides, your question makes me wonder if you're basing your views on the quality or quantity, amount or percentage (if it really isn't the art style).
Examples of anime with cute characters and/or art from 2014:
Barakamon, Fate/kaleid, Gekkan Shoujo, (Hanayamata), Brynhildr, Gochuumon, Ishuukan Friends, Mahouka, No Game NL, (Soul Eater not), Chuuni, D-Frag, Gin no Saji, Inari konkon, Nisekoi, Denki-gai, Bahamut.