My opinion is that it can be good to explore various things. Either or, in combinations - so many versions to try and see how they work, then stick with what's effective. Often one approach that has been beneficial for a while, in a certain period, is no longer helpful... move on then and try something else.
I had a couple years of "love affair" with therapy a few years ago, to the extent even that I considered training to practice a form of it part-time. I had been very curious about it for a long time prior, so went with a wide open mind. I saw a few different therapists, some only for 1-2 sessions and worked with two a bit more long-term (about a year each, and sometimes I juggled both in parallel). It was interesting but nothing life-changing or tremendously helpful for me and I often had a tendency to use it more as a distraction from actually truly dealing with my issues. I work in the mental health field myself and have always been introspective, interested in understanding how I work, self-improvement - these things come naturally to me. Surely alcoholism distorted a lot of that, certainly did not make me improve, and it took a while in sobriety also to really regain my mental clarity and balance (or develop new forms of it). So therapy was exciting for me for a while, mostly because of the mental stimulation and novelty it provided, the ways I was trying to figure out how to use it and what to make of it. Overall though, for me, it wasn't anything super useful. I stopped going after about two years total. Don't regret trying it but I doubt I would go again in any foreseeable future, I can't really see what for.
I also tried psych meds and experienced mild benefits for a while with some, with others pretty much just unpleasant side effects, and some brought a combination of a somewhat helpful and annoying. Most of my medicating was during the times when I also did therapy. I stopped experimenting with those as well.
What tends to work best for me, and I can say quite stably and long-term now, is many of the self-care approaches mentioned already above. The variety is endless really - I love to try new methods in this area. I tend to respond very well to novelty, so sometimes simply just exploring new things can give a boost of mental health. The most important factor for me though is trying to keep a reasonable balance in my lifestyle. Fortunately, I'm finding that aging (and of course sobriety) has brought a very significant decrease in my tendencies for obsessiveness, excess and extremes (I think this is very common) - it's actually pretty easy now.
I don't have strong negative or positive opinions on either therapy or psychiatric medication. What I think most important is the context, the individual person and issue. I haven't been using any professional mental health treatment now for >2 years and, in general, feel better than ever. I really think it is the much healthier and balanced lifestyle. I do experiment with nutritional supplements sometimes but not ones that are too mysterious or dicey. The only emotional challenge I continue having to some degree is anxiety... but that's also the one I have had in my whole life. A good lifestyle, including good habits and discipline, helps me more than anything with the anxiety as well.