Try this as a very quick outline? You'll be able to flesh this out with sustained discussion of Marx and Durkheim, based on some excellent introductory text like one of Ritzer's

In brief, the issue here turns on whether major social change is gradual and evolutionary or violent and revolutionary. Durkheim is closer to the former, Marx believed in the latter. Of course, there could be a difference of opinion about what counts as major social changes as well -- it is not always easy to tell, of course, especially at the time. Has the Net brought about major social change, for example? Will it? What about the trends some people call 'postmodernism' and others 'late modernity'? Partly this debate also turns on whether major social change is occurring as a result of the conditions called 'hyperreality' (for example). I suppose in general, we could focus on large changes of those aspects of life assumed to be central to entire social systems -- family, work, belief, identity, for example.

Let's start with Durkheim, who believed that societies could be placed on some evolutionary scale, with Australian aborigines, say at the 'early' end, and ours (of course) at the 'advanced' end. One dimension for change is from mechanical to organic society, from societies based on strongly held central beliefs which applied to everyone alike, to societies with much more individuality and tolerance of difference, and a set of social relations based on interdependence. These changes -- towards social differentiation -- arose because societies grew in size, came into contact with other societies (which put traditional beliefs under pressure), and eventually developed forms of work and life based on advanced divisions of labour as in industrial nation-states. Now this change need not be smooth or free of problems -- rapid social changes could bring social unrest. Rapidly industrialising societies were especially prone to excessive individualism as the old social ties weakened, and new ones lagged behind -- this leads to nasty social outcomes like anomie or rises in suicides or crime rates. But eventually, social order will and must re-assert itself as new shared values crystallise and bind people again, maybe in a new shape (e.g. nationalism
replaces religion). The State had a role in this --to preserve social order by minimising inequalities, protecting the victims of change, and re-integrating the lost sheep (especially via the new modern education system, or via the encouragement of work-based guilds -- quite radical ideas at the time). 

Let's try Marx. Societies were divided into exploiters and exploited,. In our era, this division takes the form of social classes based on the ownership (or not) of capital. 'Shared values' are really the values of the dominant groups trying to integrate and subdue the people they are exploiting --although sometimes they do offer comfort at least (as in the case of Christianity -- 'the sigh of the oppressed...the opiate of the people'). Societies based on exploitation must be unstable, though, since no group allows itself to be exploited forever. Further, technical and industrial change (especially in our era) are constantly bringing about new forms of social life which also 'denaturalises' the social order -- work in factories, shift work, changes in family life,urban living, frequent spells of unemployment or re-training, wars, imperial conquests to gain new markets, changes in the landscape, the introduction of new products, and so on. Marx emphasised these economic factors as the most important ones (arguably): as the economy gets more and more radical and innovative,  'All that is solid melts into air'.  Hence radical change takes place, led by exploited groups who seize their opportunities to displace the old exploiters and come to power. In Marx's day, the new industrial capitalists were struggling to break the hold of the old feudal lords and the land-owning aristocrats and replace them (they had done so in France in 1789 and in the new American republic of the 1770s). However, the working classes would be the rulers of the future -- they would become conscious of the ways in which they were being exploited, get organised and join together in a common cause, and realise that the tremendous productive power of industry was still being siphoned in to the hands of a few, on the highly dubious grounds that they happened to own (a majority of shares in) the factories. When the proletariat came to power, exploitation would finally end -- since they represented not just their own class but a genuinely universal social interest. Whether social change of any kind would end is more debatable -- certainly change based on the struggle of the exploited would cease, but whether some sort of evolutionary change would persist, or functional adjustments and reforms continue, based on new needs and possibilities, is more uncertain. Maybe other kinds of inequalities would persist too (e.g. gender ones?), but we end with our initial question again -- are these major forms of social change or not? Marx's answer would probably suggest that of all the currents and pressures for change, only the class struggle would change the system -- class inequality is the only kind that capitalism cannot reform away.

So - generally, quite different explanations of social changes here -- but, as with all general theories, quite different notions of social change too. If you have read my study tips notes, you'll know that I think students ought to add a few speculations of their own by way of intelligent comment at the end of their essays. Here is a couple of ideas: 
 

• Durkheim might need Marx to explain revolutionary political upheavals  he was certainly interested in Marxism and in the new society appearing in Russia in 1917). Marx might need Durkheim to explain more gradual social changes, like those occurring after revolutions make the big changes? (And more generally, marxist are better than functionalists at explaining social splits and schisms in the shared values by reference to the system level,  while functionalists are better at explaining the solidarity at the social level that must arise among members of an oppressed group if they are to take on the system and win?). If you are into this try D. Lockwood's book (1992) Solidarity and Schism: 'the problem of disorder' in Durkheimian and Marxist sociology, Oxford: Clarendon Press

• Of course, neither are very good at explaining contemporary forms of social change, you might want to argue, especially changes focused on gender or 'race', or age or region, or, for that matter, changes arising from the effects of wars. They haven't ignored these factors, but they are not at the centre of their work as factors in their own right. Weber (the other main founding parent) also wanted to stress the role of cultural factors as important in their own right -- rationalisation especially, where the technique of quantifying and calculating efficiency has a momentum of its own and can transform social life (in an ironic and unintended direction). Weber's ideas, as expressed, say in the Protestant Ethic and the Spirit of Capitalism are usually seen as ways to rectify Marx's emphasis on the economic factors in social change -- but you can use them to round out Durkheim too.