Criminal Appeals Common, Reversed Convictions Are Not

At the Trial Court Level

About 90% of felony criminal defendants who are convicted or go to trial and are acquitted resolve their cases by entering a plea bargain before trial (this may be as high as 95%). Of those felony criminal defendants who go to trial, the guilt or innocence of about 90% is determined in a jury trial, while it is determined in a bench trial for about 10%.

About 20% of felony criminal defendants whose cases are tried before juries are acquitted at trial. A far smaller percentage of felony criminal defendants tried in bench trials are acquitted at trial.

Overall about 98% of felony criminal defendants whose cases are not dismissed by a prosecutor prior to trial are convicted of something, and 2% of felony criminal defendants whose cases are not dismissed by a prosecutor prior to trial are acquitted.

At The Appellate Court Level

About 40% of felony criminal convictions following a trial are appealed (the appeal rate is very nearly 100% in death penalty cases). This is much higher than the rate of appeals of civil jury verdicts, in part, because convicted criminal defendants who cannot afford a lawyer are entitled to a direct appeal at state expense (although it can be pointless to do so if you already have a felony criminal record, you are likely to be released before the appeal is ruled upon after considering your sentence and time served, and your prospects of success on appeal are poor, which is the case in many minor felonies). 

About 8% of cases appealed in felony criminal cases result in a reversal of at least part of a trial court decision (although the figure is about 19% in death penalty cases). 

On Remand

About 7% of convicted felons whose convictions are reversed on appeal and who are then retried before a new jury are acquitted (I don't have data breaking out the retrial results for capital convictions that are reversed on appeal and retried easily at hand right now). This number, by itself, provides an order of magnitude estimate of the reliability of jury trials (although, of course, cases reversed on appeal are by definition cases whose verdicts are not reliable for some specified reason, relative to cases in which convictions are not appealed or are affirmed on appeal). 

Conclusion

So, the odds of a criminal conviction following a trial being appealed, reversed on appeal, and then retried resulting in a conviction is roughly 0.2% (one in five hundred). Thus, any given criminal defendant is 100 times more likely to be acquitted at trial than to be acquitted in a second trial following a reversal of a conviction on appeal.

On the other hand, 0.2% of criminal defendants is a pretty small share of all criminal defendants who are wrongfully convicted at trial, which realistically is somewhere in the range of  2% to 20%, implying about 0.2% to 2% of all felony criminal defendants whose cases are not dismissed by prosecutors prior to trial.

There are not very good estimates of the percentage of innocent criminal defendants who enter into plea bargains, but even if the rate is just ten percent of the percentage of criminal defendants wrongfully convicted at trial, the total number of innocent people who plead guilty is comparable in number to the total number of innocent people who are convicted at trial. Estimates range from about 0.5% at the low end to 8% at the high end.