Let me try to answer your question. (Sorry in advance if this answer gets too long.)
I used to do some criminal defense work back in the early part of my career. I practiced in a rural area, and if you were an attorney practicing in that county and you did any trial work and you didn't work for the district attorney's office, then you were expected to take court-appointed cases representing indigent criminal defendants. So it wasn't a big part of my practice, but I did enough to get my feet wet. Since I was taking criminal court appointments anyway, I also did some private pay criminal defense cases.
I digress, but I will say that part of the reason that I became a lawyer in a rural area was the influence of To Kill a Mockingbird and the ideal of Atticus Finch.
Some of the differences between private and public defenders (PDs) are small and some are large. We presume both are competent and want to do a good job. Court-appointed public defenders are paid a small fraction of the money demanded by private criminal defense attorneys. For instance, (this information is old) I might have charged a private-pay client $2,500 to defend a DWI case; whereas in a court-appointed case, the county might pay me $500.
Today, many areas, especially more populous areas, are served by public defenders offices, which are attorneys hired by an agency of the county or state and paid a salary with some benefits. (I need to look up whether PDs are paid as much as ADAs with similar experience. They should be!) But these PDs have a caseload: that is, a number of cases that they are assigned at one time. Generally, they have lots of cases and lots of clients to represent, so it is physically impossible to spend much time with any one client. Private attorneys have the luxury of spending more time because they have fewer cases, and that's one reason they charge more.
In a high-profile case like the present one, I'm sure several PD attorneys, investigators and support staff are assigned to this case. I cannot say how many other cases those attorneys may have on their caseload, but it is understood that a significant amount of time will need to be devoted to this case.
Not sure about Colorado, but in the state where I used to practice, if the case was a "capital murder" case (meaning that the punishment range included the possibility of the death sentence), then defense attorneys on those cases had to be specially certified for competency.
The defense's job is to 1) ensure the defendant gets a fair trial; 2) obtain a not guilty verdict if possible; and 3) obtain the lowest sentence possible.
The defendant gets to direct the strategy of the defense; meaning, he gets to decide whether he is going to testify; the nature of the defense; etc. The lawyer, with the assistance of the client, makes what we could call "tactical" decisions; such as what witnesses to interview, subpoena to testify, what questions to ask at trial, etc.
The defense lawyer has two loyalties here. He is an officer of the court, which means he can't lie or mislead the court or jury (he cannot put on evidence that he knows is false), and he is bound by the law and the rules of procedure and evidence. He also has a duty to inform the client of the law and the facts, so the client can make informed decisions; and he is bound to follow the defendant's stated strategy, if he can do so within the bounds of the law and ethics.
Some attorneys say you shouldn't ask the client if he is guilty or not because you don't really want to know the answer to that question. I always asked my client for their version of the facts, and I took them as true unless my common sense told me otherwise. If confronted with a situation where the client's story doesn't seem possible, then I would ask him about it (not grill). You always want your defense to seem as plausible as possible. You can't build a credible case around something that is ridiculous (your word).
In the end, I wasn't always 100% comfortable practicing criminal defense because it didn't set well with me having to establish reasonable doubt when I didn't believe it myself. There's a line there somewhere, and I wasn't comfortable stirring up confusion when it didn't seem appropriate. (Other defense attorneys can chime in here---lots of them do a great job without it bothering their consciences, and they do it ethically.)
I hope that helps. Sorry so long.
Edited for clarification
