The nature of liberalism and radicalism tends to vary, so the advantages and disadvantages of each will likely fluctuate as well.

One conventional advantage of liberalism in a social and cultural context is tolerance. Liberalism tends to be tied to tolerance, diversity, freedom of expression, and so on. Liberalism has a reputation for placing a premium on inclusivity and for countering racism, sexism, transphobia, homophobia, and so on.

However, recently, some leading figures with liberalism associations have criticized the left and liberals for promoting censorship and restricting expression. While in one light, an advantage of liberalism could be acceptance of differing viewpoints, in another light, a disadvantage of liberalism could be its noted hostility towards thoughts or information that doesn't align or reinforce a certain worldview.

Radicalism usually involves a thorough and complete transformation of society. Radicals aren’t concerned with piecemeal, step-by-step changes. They want a deep reordering.

One debatable example of radicalism is the call to defund the police. People in favor of defunding the police don’t want to try and reform the police: they want to utterly remake their role in society.

An advantage of this supposed instance of radicalism is that it faces the lethal, brutal role police have played in the lives of people of color. It also addresses the fact that police are used in situations that other professions, like social workers, would probably be better equipped to handle.

A disadvantage of radicalism—whether it involves defunding the police or another issue, like healthcare for all—is its associations. Many people associate radicalism with unhinged views and are alarmed by the term. Yet maybe it shouldn’t seem deranged for people not to want police to kill them. Perhaps it shouldn’t seem demented for people to want access to healthcare regardless of their socioeconomic status. In this light, radicalism has something like a marketing problem. What’s portrayed as radicalism is not always radical.

One of the main advantages of liberalism is that it focuses on the betterment of society—social, political, economic and cultural growth, progress, and prosperity are essentially the main goals of liberalism. According to liberals and some political analysts, a liberal system is (or at least should be) the foundation of democracy, as liberalism as an ideology is built upon the concepts of liberty, freedom, equality, peace, and protection of and advocacy for human rights (the people benefit from the state, and the state benefits from the people).

Aside from sociopolitical stability, security, personal freedom, individuality, liberalism also promotes economic development, as well as equality of opportunity and freedom of enterprise.

On the other hand, critics argue that one of the disadvantages of liberalism is the people's dependence on the government. As a liberal government tends to be very involved in nearly all social, economic, and cultural spheres, then people expect the political leadership to excel in their jobs and to make sure that the people are safe and comfortable and that the society functions the way it's supposed to function. This is not an easy thing to do: the political structure is often prone to criticism, which might result with sociopolitical imbalance. Conservatives also argue that liberalism disregards the importance of traditional values and destabilizes the cultural sphere.

Radicalism is actually derived from liberalism, as it was a political movement that united the extreme left during the French revolution, and it is also the inspiration for the creation of the theory of social liberalism. While liberalism focused on individual liberty, radicalism focused both on liberty and equality.

The main advantage of radicalism is that it promotes sociopolitical reform. Radicals (be it the radical left or the radical right) argue that radicalism as an ideology encourages the people to challenge the system, especially if it fails to meet the individual needs of the people and the general needs of the community as a whole. Unfortunately, radicalism goes hand in hand with extremism; thus, a radical democracy can either be a Utopian or a Dystopian society.

In this context, extremism is the main disadvantage of radicalism; extreme thought is either too ideal or far from ideal, which is why it's often accompanied by violence and oppression. Radicalism may promote difference as a philosophical and political concept; however, it's unclear what that difference is. While it might mean acceptance and tolerance of diversity, it can also mean the complete opposite.

Some argue that radicalized societies accept terrorism and extremist violence, which usually appears as a consequence of the people's frustration with the local socioeconomic and political climate and structure. This anger and frustration with the system and the need for a fundamental societal change is essentially the main reason why many people tend to have radical views and opinions.

The answer to this depends on what you mean by radicalism and especially liberalism (which can have totally different meanings depending on the context). I will focus on the definition of liberalism that is most commonly used today in this answer. 

Modern liberalism tends to focus on the constructive role of the state in protecting the environment, promoting economic opportunities for people, and preserving human rights. While most liberals accept that free enterprise and capitalism are to be promoted, they believe that there are some things that are best managed by the state, often because they are unprofitable for private business. Liberals also tend to promote government involvement to promote equal opportunity for minorities in ways that conservatives find inappropriate. Criticisms of liberalism often argue, in general, that it reflects too much optimism about what government is able to accomplish. They say that government programs are too expensive and often yield unintended consequences that actually worsen the social problems they were supposed to address. Many critics also say that liberalism involves excessive government intervention in things best left to the private sector, and that it stifles the economy by restricting free enterprise. 

Radicalism can also have many different meanings. Whether far-left or far-right, radicals argue that society is so deeply flawed that it must undergo a fundamental, revolutionary change. Criticism of radical positions might include the following. Many would argue that radicalism assumes the ability of people to overthrow natural human institutions, to make things anew in a way that is impossible. Others decry the violence that often accompanies radical movements. Still others would say that in a democracy, radicalism draws votes away from more realistic mainstream political movements. Finally, radicals alienate moderates, making it difficult to form the types of coalitions that make political action possible. 

Again, it is important to note that the definitions of these words change with time and place. What is radical at one point in history, or in one society, is mainstream in another.