If you are going to compare with Trello and Asana, we shall start it with their approaches in usage.
Trello is a generic tool and it is not designed specific for projects or anything else. All the column, board, card, etc.. are flexible to convert to in another usage. Therefore, Trello can not be named as a specifically designed for project or task management.
On the other hand, Asana and various tools are designed specific for task or project management. They are getting terminology and various popular way of management and their needs. There is more than one way to manage projects :) and to be honest, i can not say one is better than the other one.
Which way is the best for showing the project list?
There will not be a correct answer of this question because project management has not have just one way. Both are good products and their usages are going to be different.
In addition to this, from screen usage perspective, if your solution needs more content area, you can hide the list but it shall be still reachable. Trello is doing that by showing your all boards in another page.
If your solution wants to create more flow oriented actions based on the project name, then having a list can be a good option for starting point.
If your solution aims to show different activities and relevant communication, maybe it is good to show them like - backend development, front-end, ux, marketing... I would like to give another tool name: Slack https://slack.com/ which is taking the management part with communication and hash-tagging way. Our all activities are tasks are also in this communication tool.