The understanding that I have is that the two ideal economies you ask about are based on the work of Karl Polanyi, in The Great Transformation, first published in 1944. This argument was, in my opinion, running parallel to cultural evolutionary thought in archaeology/ anthropology at the same time, and Polanyi argued that societies went through successive stages of economic development (reciprocity and redistribution/command) until reaching full blown, modern market economies.

Even Polanyi (1944, p 56) however made space for "market qualities" in what he believed to be purely redistributive economies, which is what many people have argued Bronze Age economies, particularly the palatial economies of the Aegean and southwestern Asia, were; today, I would argue for a more nuanced understanding of these idealized types. Halstead (2011, Redistribution in Aegean Palatial Societies, p. 229) I think is very right to argue that "describing Aegean political economies as redistributive in the Polanyian sense is inaccurate and misleading." His argument, in brief, is that the idea of a redistributive palatial economy was long assumed based, in the Aegean, on the Linear B texts and their references to an influx of goods and services into the palace complex. However, as far as we know, the agricultural storage was not located at palatial centers, with the texts themselves pointing to decentralized grain storage and production. Moreover, the amounts of goods attested as being controlled by the palace could not possibly have adequately provisioned the areas that the same texts purport to control, (and this is tough, because some of the business run by the palace could absolutely have been on an oral and non-written basis), and there seems to be a fair amount of implied "local business" for which we have no formal understanding of; this could have been reciprocal exchange, as Halstead argues, or they could have been market economies, as Parkinson, Nakassis, and Galaty (2013: Crafts, Specialists, and Markets in Mycenaean Greece, pg. 414; see also Feinman 2013, same publication) argue.

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So to answer your question, I would not argue that Late Bronze Age economies, at least in the Aegean, were either redistributive or market economies, but rater a unique combination of many aspects of Polanyian "idealized economies," and I would also go further to say that many of these arguments can be extended to a number of places in Southwest Asia, where there is better written evidence; Sauvage (2011, Evidence from old texts) has described Eastern Mediterranean trade in the Bronze Age as well managed internationally, with international laws, general protection for merchants, and taxation. While these all show that international trade was highly regulated, though, they do not automatically point to a redistributive system. Though it's a bit dated by now, I personally love McGeough's (2007, Exchange relationships at Ugarit) argument for a "palatial economy," based on the economic texts at Ugarit, as this nuances and contextualizes the Polanyian ideals which have long been discussed. To McGeough, there was no "economy" in these societies, as the economy was not conceived of as monolithic. What we would call "the economy" was likely conceived of as a "network of contingent exchange relations," with market, redistributive, and reciprocal activities open to all agents within the system to some degree. No one mode of exchange controlled all economic activity, nor did any one agent control all these activities. The palace, for example, was an economic agent in McGeough's view, and a powerful one at that at Ugarit, but it did not control the economy, because again, there was no monolithic idea of an "economy" to control. Nor was the palace's position ever a given. It simply, at the time we can analyze, played a larger role in exchange relationships than other actors did. McGeough calls this approach to analyzing the economies of ancient societies the network based model.

Thus, the palaces of the LBA Aegean and SW Asia, in my opinion, dominated the exchange relationships occurring within their polities and societies, but we cannot boil down the nature of these interactions to an archetype; the reality was too complex for this, and in most cases, we can argue that the many actors involved in the exchange network (palaces, the king, elites/rich members of the nobility, merchants, priests and priestesses, craft specialists, farmers...basically anyone in the polity) all jostled, within a socially constructed understanding of what was appropriate for each individual, for power and the ability to improve their standing. Because of the many advantages offered to it through socially accepted convention, the palace generally remained on top, allowing it to impose taxes on individuals, take many goods for itself, send other agents to do its bidding, and transfer resources effectively between agents. It never, as far as I can see though, controlled every single economic activity, or enforced a free market through its abilities, because it simply was not powerful enough to do so in almost any case, and there were always agents who slipped through the cracks.