Empirically, I wouldn't know.
But theoretically, the reasoning behind a jury system has been formalized mathematically.
What does it mean for justice to be served?
There is a dilemma because of what statisticians call "type 1" and "type 2" error.
With a justice system these types of error are:
- Letting the guilty go free
- Convicting the innocent
Condorcet's jury theorem  argues that a traditional jury operating under unanimity for conviction is less likely to commit the second error than picking a single juror and making him the judge of the facts. Suppose that the probability that juror i will wrongfully convict the innocent is p[i]. Then, if we assume independence of jurors (which can be problematic), the probability that an innocent defendant is convicted by the jury under unanimity is product(p[i]; 1<=i<=N). Since p[i]<=1.0 for all i, this product is necessarily smaller than any individual p[i].
This does not answer whether letting a judge decide guilt might do better or worse either because of his training or potential for acquiescing to government demands or falling into corruption. However, it does show that at least on avoiding the conviction of innocents, a larger jury should be fairer than a smaller one.
Type 1 error is increased. The proof, I suspect, is a bit more tedious but basically the same principal with "and" replaced by "or". Only one juror's false belief in innocence (or corruption) is required for type 1 error.
These are different injustices, and trying to mold the system to reduce one error often increases the frequency of the other error. Designing for a balance between these errors involves some serious moral and ethical issues, among them the problem that citizens may have different preferences for them. While Blackstone suggested "better that ten guilty persons escape than that one innocent suffer", any balancing invites both the questions "how many innocents should suffer a false conviction?" and "What casualties do the freed guilty create among other innocents?"