Diamond Tiara is most definitely the worst pony. However, it is not her fault that she acts the way she does. Tiara is a product of her "wealthy" upbringing and was most likely taught, at a young age, to belittle other ponies as a way to increase her stature. As somepony noted above, Tiara's true self emerged during her reign as editor-in-chief of the Foal Free Press. Her goal was to find as much dirt on everypony, in an effort to demoralize them (and to sell papers, as we saw everypony loved the gossip when it first started) and provide herself with a platform to shine. Unfortunately, Diamond Tiara must suffer from low self-esteem (this is my opinion and it might not be right, but this is my analysis of Diamond Tiara)- Tiara has to constantly make herself look amazing in front of her peers, by putting other ponies down. This is evidenced in the numerous episodes where the Cutie Mark Crusaders are in the classroom with Tiara.
I would love to see what Tiara's home life is like, as it would provide us with a better understanding of Tiara and her vicious actions (does her father make fun of her, does he beat her, is she ignored by her parents and left alone in the house, is she constantly praised even when she fails at something, does she get everything she wants...there are so many possibilities and each event that occurs at Tiara's home, could potentially alter and mold her emotional state). At this point, we do not have enough information to fully understand Diamond Tiara.
As for Trixie, she is just an amazing show-off, that is cocky, brash and arrogant. Again, like I noted above we do not have enough information or background history to fully understand why Trixie acts the way she does. We know, that Trixie crumbles under extreme pressure and is prone to running away (as is evidenced in the episode Boast Busters, where she freaks out when confronted by the Ursa Minor and then later runs away from Ponyville). However, she acts very similar to Diamond Tiara when boasting and showing off. When the mane6 tried to compete against Trixie, she both belittled and made fun of them by using her magic-each time one of the mane6 went against Trixie they ended up in a compromising position. Trixie did this to affirm, in her mind, that she is the greatest wizard in Equestria.
In the end both Trixie and Diamond Tiara are very similar, however, I still think Tiara is the worst pony. Trixie is just too amazing and I would love to see her return to MLP.