Varieties of criticism
Conservative criticism has nothing much to do with "left-wing" or "right-wing", because left-wing people are often very conservative, in the defined sense, while right-wing people can also be very radical, in the defined sense. The difference between "radical" and "conservative" has more to do with the belief in whether "a change to something genuinely new" is really possible and necessary. Radicals typically believe strongly that such change is highly desirable and necessary, and that it can be achieved. Their criticism is that there is "not enough" change. Conservative critics, by contrast, are very skeptical about any such change, because they feel the change is really "just another form" of something that already exists.
Left-wing politics
The spectrum of left-wing politics ranges from center-left to far-left (or ultra-left). The term center-left describes a position within the political mainstream. The terms far-left and ultra-left refer to positions that are more radical. The center-left includes social democrats, social liberals, progressives and also some democratic socialists and greens (including some eco-socialists). Center-left supporters accept market allocation of resources in a mixed economy with a significant public sector and a thriving private sector. Center-left policies tend to favour limited state intervention in matters pertaining to the public interest.