This really depends on the person and also what their mental health problem is. It’s a bit different to physical health problems in that often mental health treatment is a case of trial and error, whereas if you break your leg you can almost guarantee the treatment will be the same no matter who you are or how you broke it!
Usually a combination of medication and talking therapies is the best course of action, but sometimes people get better just using medication alone, and sometimes they get better just by talking to someone or doing cognitive behavioural therapy.
It largely depends on the nature of the mental health issue. For instance, you would not just treat someone with psychosis with counselling. They need medication. You would not just give medication to someone who is depressed because they feel isolated.
I think it depends on the individual – some people respond better to medication, others experience no benefit of taking medication or experience some unpleasant side-effects. For others, CBT and other talking therapies are really useful, but some people find CBT and some specific therapies to not help. CBT does tend to involve a lot of homework on the individual client’s part and may require a certain level of reflection on your own experiences, which some people may not be able to do (if they’re particularly unwell) or find unhelpful. There was a big trial of CBT for people with bipolar disorder (who were currently experiencing quite severe symptoms) – the trial didn’t show any big benefit of CBT over what the individuals were currently receiving in terms of therapy. I think we need more research to understand how these therapies work and who benefits from them (and why)… focusing on the individual’s needs and what works for them should be key (and may mean more medication… or more talking therapies… or a combination of the two)