Best male anime character:
Araragi from Tsukimonogatari/monogatari series in general, which would include this year's Hanamonogatari.
I don't want to draw this into a lengthy comparison and this is all my opinion, but I just don't view characters coming out of shonen action/fantasy with the same level of respect or interest as someone like Araragi. I won't deny that their is something inherently appealing about a character trying to get "stronger," which is what most of these shows focus on when employ that motif, but after a while it's difficult to really relate or care about protagonist x, y, or z's struggle with power or responsibility in that straightforward of a manner.
So, I wonder to myself what does Araragi have going for him as a interesting character, and I think that's a product of the writers and studio creating the character in such dialogue heavy franchise in which facets of life like conflict, relationships and maturing are discussed with relative depth that you don't see elsewhere. I envy the way the Araragi interacts with other characters who are either his mentors or peers in different regards, sometimes learning from them, but other times giving out advice. In Hanamonogatari, Araragi acts as the senior and assists the main female protagonist Suruga, but in Tsukimonogatari(more so as a result of the passing of time), he needs the help of Kagenui to identify and handle that crisis. Another thing working in Araragi's favor is Ougi, a character that without going too much into it, can provide exposition and criticism towards Araragi's actions and mentality. Of course their is nonsense within the series, all the incest bait and stuff, but you realize that those are such blatantly comic grab bags that you can ignore it.
Tsukimonogatari explores Araragi's usage of power, and the consequences of creating a habit from relying on something that is not totally within his control, to overcome the various oddities. I can't stress enough how lengthy bits of dialogue change this from being some sort of generic action plot device, into a full dissection of a character's acceptance of prior actions and maturity to understand and face a new obstetrical in a completely different way than his prior engagements. Sure their is a villain that needs to be stopped, sure the villain did a bad thing, but I challenge any other anime to put a more interesting antagonist on the table as Teori, who is shown for maybe 5mins in total.
Best female anime character:
I could go with the 5 mins of Senjou, but rather I'll give it to Akane from Psycho Pass 2. Sure the second season suffered from a staffing change and 11 episode rush to fit as much content as the first season, however I'll give my due respects to Akane for growing as a character and challenging the sibyl system from the inside.