Does the evidence support the idea that he massacred innocent civilians at Drogheda and Wexford, or is it more likely to be Catholic propaganda, in the same vein of the reported murdering of 100,000 protestants being murdered by Catholics in the 1641 rebellion when there were not even that many Protestants present in the country at the time?
As an Irishman I was woefully unaware that this was ever even a question. It is taken as common knowledge here that Cromwell was a butcher who murdered his way from one town to the next, accepting surrenders from cities and then butchering the inhabitants.
I have recently discovered that outside of Ireland this is not the opinion at all, and there is evidence to support the idea that Cromwell was better than most of his contemporaries at sparing civilians due to the rigorous disciplining of his troops.
Which of these ideas holds more weight in the historical community at large, or does the truth lie somewhere in between?
The answer is somewhere in the middle, though I would argue that the reality is closer to your original opinion than the kinder view. The best work on this is chapter 4 in Hutton, Debates in Stuart History, which I will draw heavily on.
Cromwell had a decidedly negative reputation for most of the last ~360 years. He was written of as a "self-seeking adventurer associated with usurpation, destruction, desecration, religious fanaticism leavened by hypocrisy," (Hutton, p. 95). Under Victoria his reputation was rescued by dissenting churchmen, and they tried to hail him as a champion of religious liberty - something that is still (perhaps wrongfully) associated with him today. Current historians, like Barry Coward, Sean Kelsey, Ian Gentles, and Peter Gaunt, have tended to present Cromwell in a more positive light (Coward, Oliver Cromwell; Kelsey, "The Trial of Charles I," Eng. Hist. Rev. 2003, pp. 583-616; Gentles, Oliver Cromwell: God’s Warrior and the English Revolution; Gaunt, Oliver Cromwell). These works are a useful tool for understanding Cromwell in Great Britain, but their treatment of Ireland is usually given short shrift in comparison. Coward present's Cromwell's opinion of the Irish well, quoting him at length stating "You [Catholic Clergy] are a part of Antichrist, whose Kingdom the Scriptures so expressly speaks should be laid in blood...and ere it be long you must all of you have blood to drin; even the dregs of the cup of the fury and wrath of God," (p. 73).
In terms of scale, the common argument of Irish that he slaughtered civilians by the tens of thousands is an exaggeration. Wexford certainly saw the death of 2,000 people, and about 3,000 died at Drogheda (Gaunt, pp. 84-85; Coward, pp. 73-75). The best works covering Cromwell's conquest of Ireland are Ó Siochrú, God’s Executioner: Oliver Cromwell and the Conquest of Ireland and Canny, Making Ireland British, 1580-1650. Most of the above authors don't make excuses for Cromwell's treatment of the Irish. However, when they bring Cromwell into a larger European context, they are able to minimalism his actions. Peter Gaunt states that Cromwell's actions were in line for much of the fighting during the Thirty Years War. Patrick Little describes it well, when he explains that though Cromwell was in Ireland for about 40 weeks, the violence he was responsible for created a black myth that persists to the present (Little, "Cromwell and Ireland before 1649," in Oliver Cromwell: New Perspectives edited by Little, pp. 116-7).
Cromwell was not personally responsible for the destruction of Ireland. He was only in Ireland for a brief period in 1649-1650. It was throughout the 1650s that the slaughter of Irish occurred on a massive scale. I wrote an answer here about the loss of life in Ireland from 1640-1660, and the number is staggering. About 300,000 people died in Ireland during this time, due to warfare, disease, poor harvests and deportation (the estimate for this is about 50,000 people - Gwynn "Cromwell's Policy of Transportation," Studies: An Irish Quarterly Review, 1930). This was mostly done in Cromwell's name, though not necessarily with his authorization.
A Jesuit, Father Quin or Quyn, wrote to the Papacy in the late 1650s a “State and Condition of the Catholics in Ireland, 1652-1656,” which helps explain the situation:
The Cromwellians, therefore, connived for a time at the liberty of the priests and the exercise of the Catholic worship, until a favourable opportunity presented itself of giving full vent to their malice...What one soldier spares to-day, is devoured by another soldier tomorrow...To crown our other miseries, the plague is raging in all quarters...whole cargoes of poor Catholic are shipped to Barbadoes and the islands of America, that thus those, whom shame prevents from being murdered by the sword, may fall under the doom of perpetual banishment...(Lynch, Cambrensis Eversus, edited by Kelly, 3 volumes, 1:80-83).
White the above source is clearly biased, it also provides an explanation for why Cromwell's name is so tainted in Ireland. Quin refers to the soldiers as Cromwellians, and it is the Cromwellian government that executes these orders. The slaughter and destruction is the legacy of Cromwell in Ireland in part because of Drogheda and Wexford. But the majority of the iconoclasm, slaughter, deportation, enslavement (as they called it), and destruction was carried out over the course of twenty years after the 1641 rebellion.