No attorney, public defender or private attorney, can guarantee an outcome. Public defenders are often overworked. In many jurisdictions they carry a very heavy case load and sometimes have less time to devote to each individual case than a private attorney might be able to do. But that does not mean that public defenders are not "good" attorneys. Many excellent attorneys choose to devote their careers to public service because they consider it to be a special calling.
If you qualify for the services of a public defender, and if you cannot afford the $2000 the private attorney would charge, you shouldn't be afraid to use the public defender. On the other hand, if you feel that the private attorney would devote more time to your case, then hire the private attorney.
The most important thing to bear in mind is that no attorney can guarantee an outcome. In any event, you do need an attorney even though this is a misdemeanor charge.
Best of luck to you.
Please note that this answer does not constitute legal advice, and should not be relied on since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship. You are strongly advised to contact an attorney to obtain legal advice before taking or refraining from taking any action with respect to the above.
Please understand that I am licensed to practice law in Texas, and no other state, and any answers that I provided on AVVO are based only on my knowledge of Texas law and not on the laws of any other state. Furthermore, nothing in this answer is legal advice and should not be construed as such.
First off, don't go back to that lawyer. Any lawyer who tells you they can get your charges thrown out is lying to you because no results can ever be guaranteed--certainly not a dismissal. Second, whether a public defender is better or worse that a private attorney depends on more factors than can be discussed here. Where I practice, there is no public defender's office and most of the private criminal defense lawyers also choose to have their names placed on the Court's list for court appointments (cases where the defendant cannot afford an attorney).
I cannot speak for anyone else, but all of my client's get the exact same representation from me, whether they have paid me $2,500-$5,000 for their case or the court appointed me to represent them and I will be lucky to see $500-$1,250 for all my work. I would suggest you meet with several lawyers and find one who you trust and that you think will represent you to the best of their ability and do their best to protect your interests (including your long term interest of keeping a clean record).
P.S.: I cannot stress enough that you should run from a lawyer that guarantees you an outcome.