Daenerys is nothing like Rand, primarily because Rand does everything that he does because of prophecy. He doesn't conquer nations because he wants to, and he doesn't even channel by choice. Instead he was forced into that position, and simply tries to do the best job he can in order to defeat the Dark One.

Daenerys does not know of any prophecies concerning herself, she is motivated simply by the belief that she is the rightful queen of Westeros, and needs to conquer it anew, and take it back from the "Usurper". But how is this motivation anything other than a convenient (and hypocritical) excuse? Westeros does not belong to the Targaryans. They conquered it 400 years ago, defeating the various rulers that lived there at the time. Those rulers had in turn taken it from the First Men, and the First Men had initially taken it from the Children of the Forest. Each group conquered the previous one and took Westeros from it, following the simple rule of "might makes right". Therefore, Robert isn't an usurper any more than Aegon was. He simply defeated the current rulers and took it from them.

I would have no problem with Daenerys going and reconquering Westeros because she wants her home back, or wants to be a queen, etc. The only problem I have with her is that she uses hypocritical excuses to justify it. Furthermore, by conquering and usurping the throne of Meereen, Daenerys has become a usurper just like Robert, and yet continues to believe that she has the moral high ground against him and his "dogs".

As for what you said about Daenery's "justice" it is a very skewed form of it. She conquers cities and kills their rulers and frees their slaves. This isn't a bad thing by itself, since slavery is a bad thing, so stopping it is good. But she fails to consider why slavery existed in those cities to begin with, and what would happen once it was gone. She didn't consider that slaves are the only exports the slave cities have, and that without them to sell they would starve and die out. Instead, she followed her sense of "justice" and did an act of good that led to consequences worse than the initial evil. Going even further, she chose not to stop people from following her, despite knowing that she had no way of feeding or caring for them, and knowing that she would have a long journey ahead of her. So not only did she willingly allow people to follow her to what could very likely be their deaths, she failed to even prioritize her own goals and objectives, something that a queen cannot do. If she continues to exhibit the same lack of leadership ability in Westeros, she'll simply ruin it as well as Cersei and Robert did.

And to give another reason for why I dislike her, and also why Daenerys is nothing like Rand, there is her relationship with Daario. She understands that he is a sellsword, and therefore neither honorable or caring, yet she bangs him anyway, and toward the middle and end of the book even starts having feelings of something like love for him, as opposed to merely lust. And she starts seeing him as much more trustworthy than he actually is. These are not things that any decent queen - or any sort of ruler - should be doing. Since you compared her to Rand, let me point out the Daario equivalent in Wheel of Time. That person is Berelain, who tried to seduce Rand. And he turned her down, despite her being one of the most beautiful women in the world. So while Daenerys can't even think straight with her beloved Daario, Rand stayed in control of himself.

Btw, while Daenerys is kind to her followers, she has no reason not to be. The only reason Rand started being an asshole to people is because he wished to protect them, since he has the Dark One constantly after him. Since Daenerys doesn't have to fear any such thing, she has no reason to push away her companions, so your comparison is moot.