Plusses: Access provides some excellent control over data, will not allow you to enter invalid data or the wrong kind of data, can enforce constraints without any need for vba, and is easier to design for other users to use. It can handle more data, of course.
Minusses: You will need to learn at least some basic SQL and database theory if you really want to understand Access. Most books on Access start with a chapter on database theory, and it is important to know at least what a primary key is and how table relationships are defined. If you create databases without keys, you are not creating an effective database. I suppose creating reports with Access can be a bit of work, too - I try to not get too fancy. This is also something that takes time to learn.
A final thought is that you need to be careful of users getting at the table data - typical Excel users might not realize that databases make changes "immediately" (there is no "close without saving changes" when you close Access) - so you have to think about who uses the data and how will they work with it. Of course with Excel, you also have to worry about who might use your spreadsheets improperly too.
I'd suggest you add Access to your toolbox - a little SQL can be a very powerful tool. Its worth the price of a class or other training, to do it right. In my opinion, using Access for data storage and Excel for data analysis and reporting can be a powerful combination.
Regards.