Some court appointed attorneys are pretty good attorneys and can sometimes be just as good or even better than a privately paid attorney.
But if possible you should research attorneys and get a privately paid attorney to represent you and your case especially if it's a pretty bad case that needs a lot of defending in court.
Say for example you're accused of murdering someone and your own life is literally at stake by you being sentenced to prison for 25 years to life or to death.
If you were not the one that actually killed the person then you would want a good paid for attorney to get you out of that situation.
If I can afford an attorney for anything I need to be defended for I would hire a private attorney who would be willing to defend me because they're being paid by me so they have more of an interest in winning the case for me.