Evolution - BraixenFennekin evolves into Braixen once it reaches level 16. Braixen at this point, remains only a Fire type. The greatest change you will note is that once Fennekin evolves into Braixen, it is no longer a quadruped. It becomes bipedal, walking upright on two legs. Braixen does still retain many of the features that Fennekin originally showed. The color scheme remains the same, with the exception of the legs now being dark grey in color. Braixen's main body color is still a creamy yellow, with the fur around the hip area fanning out to mimic the look of a skirt. Braixen still has the dark orange ear fur (which has grown significantly longer), and the tip of the tail remains dark orange as well. The area of what fur has expanded from just being around the muzzle to reaching up higher on the head, and around the chest and arms. Braixen's nose is dark orange, no longer the grey color that Fennekin's was.
Another additive change that was made was the stick/wand that is placed in the tail fur. This sticks to Fennekin's theme of loving twigs, but instead of eating them, Braixen uses the stick as a wand to cast her fire special attacks. The stick is removed from the tail in these instances, and according to the Pokedex, the twig is lit on fire because of the friction when being removed. The flame can also be used by Braixen as a means of communication. Braixen reminds me very much of a little witch. This fits very much with the idea that the starter Pokemon of this generation are meant to mimic a Mage (Fennekin line), Rogue (Froakie line), and Knight (Chespin line). Braixen still looks a little bit juvenile to be a mage yet, but I think that is quite fitting for a middle stage evolution.
Evolution - DelphoxBraixen evolves into Delphox at level 36. At this point, the typing switches from solely Fire, to Fire/Psychic. The changes between Braixen and Delphox are pretty noticeable, even though they clearly keep to the theme and color palette. We can see that the fur on Delphox is significantly longer than it was on Braixen. It now resembles at magician or mages robe, with the primary color being a very dark orange (darker than we have seen before). The long sections of fur now cover the legs and arms, with only the tips of the dark grey feet/hands showing. The original dark orange color is still present in the now-huge ears, and on two flame-shaped sections of fur on the legs. There is no longer a dark orange tip on the tail. The white around the muzzle has decreased back to the amount originally shown on Fennekin, and there is a long white section that hands in the center of the chest area. The rest of the upper chest area (barring arms) is covered with the primary cream yellow color, in a vest sort of fashion.
The stick that Braixen was keeping in its tail is now wielded in Delphox's hands. It is no longer kept in the tail at this point, but is stored in the 'sleeve' fur when not in use. According to the Pokedex, Delphox is able to achieve a focused state by staring at the fire at the tip of its wand. Using this focus, it is able to create extremely hot spirals of fire (possibly mystical fire) with its psychic powers. Supposedly, Delphox is also able to view into the future by staring into the flame as well. Delphox very much resembles a wizened mage at this point. It has become larger, and the facial features have become much sharper. It looks a little less 'cute' and a little more serious.