The reality, and to some extent the conventional wisdom, is that jury trial as less accurate (and jury trials are without a doubt, in modern times, less efficient).
But there is also a widespread belief that jury trials are less biased than bench trials. Judges are probably more accurate but are perceived as being biased against most kind of criminal defendants, so that the average result is worse of innocent defendants, even though jury trials probably cause more guilty defendants to go free than they would otherwise. The empirical evidence is mixed and is system and context specific (judges might be biased in favor of law enforcement defendants, for example). But the revealed preferences of criminal defendants show an overwhelming belief that the average results of jury trials for them are better than the average results of bench trials for them.
The fear of judicial bias also illuminates the circumstances under which the British retain civil jury trials (e.g. in eminent domain valuation proceedings, where judges are seen as having something of a conflict of interest since their department's budget competes for scarce funds with those funds used to pay eminent domain claims). Sometimes being fair is more important than being right, and that is what the jury system strives to do.
The belief that judges have some inherent biases overlaps with the notion that the jury may bring a broad range of insight into interpreting the factual presentation and the credibility of witnesses based upon their wider range of personal experiences.
The removal of the class and occupational biases of judges generally from the system also does have a democratic aspect to it. It gives granular active control of a key form of state use of power involuntarily over someone to the democratic populace making the system more democratic.
Juries also turn a decision made by a lone judge (because unlike civil law systems, common law judges with only rare exceptions conduct bench trials individually, rather than in panels of judges), guarding against the idiosyncrasies of any one individual decision maker. Also, as a practical matter, in the U.S. and pre-modern England, there was a scarcity of legally trained judges so adopting a system calling for far more judges per capita, as civil law legal systems of Continental Europe did, would have been expensive, and juries made collective decision making possible, leveraging scarce judicial resources.
Another important facet of this is jury nullification which gives a jury the practical, although often not formally acknowledged, power to disregard the law when its application seems unfair. The revolutionary Americans figures that their fellow citizens would be less likely to convict them of wrongs against an unjust state than British appointed judges had been to do so, and in practice, even in modern times, juries have often been lenient with politically motivated criminal defendants charged by the state with crimes.
It also reflects a political calculus on the part of the judiciary collectively. In a bench trial, the public will seek to hold the judge responsible for decisions with which it disagrees and to blame the judiciary collectively for bad decisions. A jury trial deflects blame from the judge to an effectively anonymous and ephemeral group of ordinary citizens so that decisions perceived as bad don't taint the long term reputation of the judge with the public. More generally, bad decisions in high profile court cases can undermined the legitimacy of the government as a whole if made by a judge, but not nearly so much, if made by a jury.
Finally, there are decisions that mosts often come up in tort cases (such as personal injury cases, defamation cases, and money claims for violations of civil rights) where a big component of any damage award involves compensatory non-economic damages (e.g. for pain and suffering and damage to dignity) and non-compensatory punitive damages claims, where a jury serves what amounts to an opinion survey-like role by translating intangible harms into fixed sums of money in a way that reflects community opinion, where there is no easy way to define that sum of money in a flexible way to cover myriad situations that a judge can follow in a principled way.
