All the terms involved – left and right, conservative and progressive – are slippery and relative. In the United States the movements described as “conservative” and “progressive” are in fact messy patchworks of both tendencies.
So let’s nail down the terms: in the Western world, what we shall call “progressivism” is the conviction that human societies are to be ruled by the universal dictates of reason, and reason alone. It has been the governing ideology of the West since about the 16th century. Against it is what we shall call “conservatism” which is convinced that human societies should be ruled by tradition. The conservative is not opposed to the laws being reasonable, but he is more pessimistic than the progressive about the capacities of human reason.
Both positions are inherently unstable. Progressives are utterly convinced of the reasonableness of their position, even if the rules of reason are often changed. What is progressive one day can become regressive the next. For example, progressive Americans in the 1920s and 30s thought eugenics was a wonderful thing and lampooned as backwards and anti-scientific Evangelicals and Catholics who thought surreptitiously sterilizing blacks and natives was a bad thing. Conservatives for their part often find themselves defending positions that their conservative grandparents would have thought obscene abominations, just because the position is a few years older than they are.
Since the West is deeply influenced by Christianity, it should be pointed out that the church is an excellent example of an inherently conservative community. It is not a product of the universal dictates of reason, but a historically contingent human community which strives to maintain and practice the traditions it attributes to its divine founder. Authority exists in the church to serve this end. While the church might at times find itself attached to progressive causes, it can not be described as inherently progressive.
An example of an inherently progressive institution might be the old Soviet Union. It does not matter how temperamentally conservative Russians may be, the entire Communist project is about the total rationalization of human society. It claims to be a purely scientific system and the universal goal of human history. It rejects the division of public and private spheres, sees tradition (the superstructure) as the enemy, and acknowledges no boundary of nation or race. If you should overturn a rock and find a Communist, he will argue that the problem of the Soviet Union was not that it was too Communist, but too Russian, that is, too historically conditioned.
One might flesh out the positions like this: conservatives love concrete communities, progressives love government. Conservatives are drawn to the particular, progressives to the universal. Conservatives see law as maintaining stability, progressives see law as transforming society. Conservatives are patriots, progressives are internationalists. Conservatives invoke the past, progressives the future, and so on. Of course I am oversimplifying, but these are the general lines.
Which is position is more authoritarian? Neither, I think. The conservative places authority outside himself, the progressive ends up placing authority in himself.
The conservative obeys the authority of tradition, and those powers which he sees as being instrumental in maintaining the tradition. He respects the authority of parents, of priests, or kings or presidents. But since in the conservative mind social norms by definition are not created but received, those authorities are necessarily limited. Authority figures derive their authority from the tradition and are subject to it. If they step too far outside of the tradition, they lose their perceived legitimacy. Revolutions are often fought not because the leaders are seen as too conservative, but as too progressive. When pushed, the conservative can get ugly. For the sake of his nation or tribe or way of life he is capable of great violence.
The progressive obeys the authority of reason and refuses to acknowledge traditional authorities, and because of that will style himself anti-authoritarian. Since the rationality which the progressive obeys is identical with his own opinions, the progressive is always disappointed to find that people disagree with him and his most rational opinion is treated as just one voice among many, so he dismisses everyone who disagrees as either too stupid to follow the argument, or too evil to admit he is right, or both. When he finally achieves authority the progressive can get ugly. The stupid and evil people who disagree and attempt to slow the march of progress will get their comeuppance. For the sake of his ideal society, he is capable of great violence.
Law always implies the threat of violence. Push the law, any law, hard enough and you will either get yourself killed or you will win a revolution. A conservative will multiply laws to protect his way of life, a progressive will multiply laws to achieve his ideal society, so both are capable of growing a police state.
If the conservative has any advantage, it is that he should, in theory, recognize the limits of law and authority. He does not expect the perfection of human society. There are some things that law simply cannot do. There does not seem to be any such limit in the progressive mind.