Having a re read of the old comics i still have along with the collected editions i have, i still find myself disagreeing with anyone who says Power Girl has been inconsistent in her characterisation. There have been inconsistent things with DC's Modern Era ( 1986/7 to 2011 ) Powergirl but it wasn't her characterisation, which even the worst writers to handle her seem to have more or less interpreted correctly on some level. What was inconsistent were her powers, and of course, her background that switched from Kryptonian to mystically enhanced Atlantean, and back to Kryptonian over 23 years.
The interesting thing is that back in the late 1980's she seemed a much more raw character, uncertain about her place in the world having lost her original Universe and also wanting to be taken seriously as a Superhero, resulting in her trying to present a confident -verging on aggressive- front that badly hid the fact she was hurting from life changing events, and distracted people from that she was actually a nice person with a temper and a sense of humour.
It's this that i guess can cause the mistaken interpretation that her personality is inconsistent, when i would argue it is layered. At times she has been laid back and witty, other times hair trigger tempered and stroppy, she can be wickedly humourous or determined to maintain her dignity even when things have gone very stupid or weird. All this and more made her seem a more genuinely human character ( since who is calm and happy all the time ? or miserable and angry all the time ? no one in real life behaves in such a limited fashion, and nor should a written character be any different. ).
By 2010, having gone through so many changes in her life, ranging from nearly dying and losing the bulk of her powers to displaying random powers and abilities such as being able to manifest mystic armour or developing peculiar vulnerabilities to 'natural materials', losing various people of importance to her, having a child and losing the child to circumstance, recovering her kryptonian abilities, nearly dying again, being a long time member of both the Justice League International and the Justice Society, and even bumping into the Earth 2 version of herself, she finally comes across as a much more genuinely assured and confident person. And this is arguably the very thing she had wanted to be and she had grown into, yet still displaying all of the varied qualities of her personality ( Palmiotti, Gray and Conner did a great job accommodating those aspects in the Power Girl solo series, and still made her seem actually confident rather than acting confident ).
And this was pretty much where Powergirls story ended i guess, as an accomplished hero, which is as good a way to conclude it as any.
Anyhow, very little she had ever done or said over the years felt like it was worryingly out of character, in the context of the time her behavior made sense and she always came across as Power girl. Even when some writers chose to ignore large parts of her continuity ( generally they ignored her time in the JLI, which i still think was deliberately down played in significance to her during her time in the JSA comics, although it was pleasingly revived both in 'I Can't Believe It's Not the Justice League' and finally in 'Justice League Generation Lost'. Ultimately I'll always think of her as a Justice League International member rather than as a Justice Society member ).
Of course this is all purely my interpretation of the character, but it's a positive interpretation.