This is strange perhaps to some who loved Leliana in DAO, because I also loved her in DAO but I always thought of her "true" internal character to be the way she is now in Inquisition. In other words, in Origins she was just "looking for herself", trying to understand her own nature, her identity, almost like an adolescent, she was a bit too naive in Origins at times (Morrigan often reminded her but of course Leli would just try to comfort herself by replying something soft and girlry-girly, I'm-seeing-the-world-with-glasses-made-out-of-roses).
In Inquisition I feel that the Leliana we're seeing is the blossomed one, the true Leliana. In Halamshiral the Inquisitor comments to her directly about how she seems "different" than back at Skyhold, and Leliana replies something along the lines of "It's The Game...". And more to it, I don't recall the whole reply, but essentially she puts on a mask even though she does seem to be more in line with her Origins' demeanor at that point, which leads me to believe that indeed in Origins she was wearing a mask but she herself wasn't fully aware of it yet. In Inquisition she accepts who she is. Additionally, during the Mage support arc, in the future part she sacrifices herself, and back at Skyhold eventually you can have a conversation with her, in which you tell her how she was in that future, and instead of perhaps being "surprised" of her actions, she understands why her future self did it and even replies that she'd do the same again (which does cement in my book how Leliana is fully "herself" now and understands her own true nature and merely accepts it and "lives with it because that's herself").
I'm saying all of this because - to me anyway - Leliana in Inquisition seems more mature, more "aware of herself", less innocent.
And, I do like her as an Adviser, but I like all three anyway because they're specialized to their own "profession", their own tactics. We have Cullen who prefers a direct approach, he's the usual "military guy", just as Josy puts it in Haven if you ask about her opinions on the others, she replies that indeed Cullen sometimes can appear like a hammer to whom all problems turn out to be a nail (or something like that). But that's fine, that's Cullen's job, his specializtion, he wouldn't know (or "know well enough") on how to approach problems with "other" types of solutions. As for Josephine, well, she's a diplomat from the inside out, so she approaches situations with elegance, politeness, tact... and more importantly, words (but words that aren't wasted and are used for the task at hand). And Leliana is the spymaster, her solutions involve "the shadows", being subtle, secrecy, deception, and for more extreme problems; lies or assassination (she'd do it herself without hesitation if necessary).
I for one like them all for different reasons when presented with different types of problems. If I need a settlement, village, trade road guarded I'll ask Cullen to send troops. If I need anything solved that revolves around nobles, kings, queens, princesses, or if I need an alliance be done or a trade agreement... I'll ask Josephine. And if I need some lost artifact be found "discretely", if I need to track down someone, if I need a subtle approach to avoid direct association with the Inquisition, if I need "someone dealt with" specifically, then I'll ask Leliana. All those problems show up eventually sooner rather than later during the entirety of the game's duration, and all three Advisers can be (and are) used. So all three are useful for their own purposes.
Now as far as my favorite goes due to their own individual personalities... I don't know. The thing is they're on duty at the war table, they're not taking a break. It's like you, in real life, at work, are you the same person at work when compared to when you're back home? Perhaps, or maybe not (maybe you think you are, and you aren't because you'd need someone else to tell you to realize it). I honestly think that I do like them all equally. I do understand, however, how some people think that Leliana seems to be "darker" or at least less "lovely" than she was in Origins, but back in Origins I for one always felt that she wasn't her true self anyway. Still, I admit, I loved her in Origins nonetheless... and love her the same in Inquisition.