This is an interesting question, and the answer has as much to do with timing as anything else. A Tale of Two Cities is set in two locations, of course--London and Paris (or St. Antoine). Charles Darnay was born into French nobility but emigrated to London when he disowned his heritage and inheritance. While others were on trial in both cities, Charles is the only character we meet who is on trial in both places. How they treat him is indicative of how they treated others.
The English courtroom is quick to hang, for sure. They're eager to hold people accountable, and they're eager to see people get their just desserts. The judges are severe and the rules are precise. Evidence is important but not necessary--or at least not subject to intense scrutiny. The room is packed and buzzing--literally and figuratively--with the people who are waiting for the next hanging. When the verdict is "not guilty," they are not angry or upset, but they are disappointed.
In France, the courtroom of the Revolution (more than a decade after Charles's English trial) is not nearly as orderly. The "judges" aren't particularly judicial or formal; instead, they are the upper echelon of rebels, but they are rebels nevertheless. The room is full of malcontents and rabble-rousers, and the sight of an aristocrat inflames their anger and a riotous eruption lies just below the surface. Evidence doesn't matter much--unless it helps convict an aristo. The verdict is all but a certainty before the trial even begins, though the release of Charles at his first trial is a joyous occasion. But that only happens once, and it is a rare thing.
The difference, then is a matter of circumstances. Things were bad in England, but the rules of order and civility in the courtroom still applied. In France, mob rule was in full force both inside and outside the courtroom.