Asana's great for us. We use it with our team here at SavvySME. Some little annoying points to it but as with any product.  

I would say that it is worthwhile trying out a few to see what works best for you. Most have a free trial or a free version with limitations.

I’ve personally used Trello and Asana. I like them both for different use cases. I think Trello is fantastic for keeping track of solo projects or small group projects (5-8 people).
I really like Asana for managing a team (10-25 people). I think Asana has better features for team dynamics. I really like the “Timeline” view to see how tasks are cascading.

I have used larger product suites such as Jira+Confluence and Rational Team Concert (an IBM product) but both of those are cumbersome and needlessly over complicated. Again, I think the best course of action is choosing a product that you and your team are comfortable with and can use efficiently, because if it isn’t comfortable it won’t make the team more efficient, it will make things even more complicated.