Excel and FileMaker are two quite different programs. Each will do some tasks very well and others not as well. I would think that FileMaker would be a much better option for what you describe, but if you are new to FileMaker and very familiar with Excel, you'll have a period of adjustment where you'll need to learn not to try to use FileMaker to do something in the same way you would with Excel.
Note: you can download a 30 day trial copy of FileMaker for free and that would be the best way to evaluate if this application is something that will work for you.
I'm trying it now but it looks quite difficult to use for me.
I'm discussing with a freelance programmer for the project now.
I have replaced Excel worksheets with Filemaker many times. If you are using Excel as a database, Filemaker can definitely be used instead of Excel.
I replaced a simple spreadsheet with a database. I wanted to add more info to each record. I could do this with Excel, but in Filemaker I could create a layout that was more concise and did not require scrolling to the right. I was able to add a drop down to field to better (and easier) add the info.
I was handed a number of worksheets. I combined these "tables" into one file. With a menu bar I can easily switch from one table to the other.
the key word is relational, excel is not a relational database application