Transition, here is my Excel/Access comparison..and I have been using both for nearly 9 years now..
To start let me say that other than size restrictions, you can pretty much do the same functions in either program, though Excel is a bit more user-friendly at first.
Excel is best stuited for fast, smaller, changing types of analysis and reports. When I say changing I mean flexible in terms of being able to run reports one way, and change a parameter..like running a sales report by a region, then changing it to a district or store. With a 65k row limit, the size of the data you are working with can become an issue, and even pivot tables and filters, two of the more powerful functions in Excel, don't work too well with too much data, even if it is less than 65k rows.
Access can handle huge, huge amounts of data. There are really 4 key parts to Access files. Tables are simply raw data, often imported or linked from other programs, like Excel or one of many ERP software packages. Tables can be sorted in a variety of ways, but generally lack the flexibility you get in an Excel file.
Tables, however, can be used in queries, which to me are the best feature in Access. A query in Access is like a pivot table from Excel on steriods. Queries can be used to extract data from tables, to add data to tables, and even to remove data from tables ( such as removing duplicate records). Query outputs look like tables, and can easily be imported or copy/pasted into Excel files for report manipulation.
Forms are a nice feature in Access that let you customize data entry screens or query parameter screens. Sub forms can be used to make more complex forms, but that starts to get a bit technical.
Reports in Access are not my favorite feature. Typically reports will be used to show the output of a query or queries in a much more presentable form. Again, although I do have some reporting set up in Access, unless I am dealing with large databases, I simply export the results of my queries into Excel and make it more presentable there, I find that to me much faster.
Access could easily handle your multiple email mailing lists...you could make each one of them a seperate table, and run a query, with company name as a linked (common) field, where it would list out each table the name appears in.
Hope that helps!