Convicted defendants generally shouldn't use the lawyer they had at trial on appeal. Rather, an experienced appellate lawyer almost always provides the best chance. While some lawyers can be effective both at trial and on appeal, criminal lawyers are generally sorted into trial and appellate specialists. Trial lawyers usually have expertise that appellate lawyers don't, and vice versa.
It can also be a benefit to get a fresh pair of eyes to evaluate a case. For instance, a new lawyer won't be emotionally invested in an argument that trial counsel emphasized at trial. Further, a frequent method of challenging convictions is to claim that the trial attorney provided ineffective assistance of counsel. The trial lawyer won't be able to determine whether that argument is viable, much less present it.