Did some research for a friend looking into the pros and cons of Basecamp vs. Monday.com for project management specifically with his company. He currently uses basecamp for setting up his client projects and team communication. His clientele is very project-oriented, meaning that each client requires different equipment and so each project has to be setup manually.
I thought it'd be interesting to share the conclusion:
Though I am a little bias toward Monday.com, Basecamp comes pretty close and for the current size and offering of your business, I think overall, if you were to stay where you're at with the company, Basecamp is the best choice - seeing that your team is already trained on it and you know how to set up projects, the benefits that you'd get from using Monday.com would take longer to pay off.
That being said, considering you're probably growing your company, Monday.com, in the long run, will be the best choice with to how customizable it is.
Basecamp is really targeted toward simplicity. With getting a working project up and running as soon as possible, but not allowing for that much project set up or customization and has limited external app integration.
Monday.com's primary focus is being intuitive while being super-advanced, with a heavy focus on the end-user - your team.
One of the things I think you'd greatly benefit from switching to Monday.com is the project timeline setup - setting up gantt charts with dependent tasks will let you better see at a glance where each project is at any given moment.
Plus allowing you have templates that you can copy and paste to each client, making it really easy for you to hire someone to take over your position where the questions are already outlined and all they have to do is fill in a couple of boxes. As well as having fillable forms that are built directly into Monday.com makes it very easy to do it on the spot from your phone.
External reference material on top of my own experience: