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This is the Wikipedia page http://en.wikipedia.org/wiki/FileMaker
Google "filemaker vs access"
The Computer Guy, Seattle
Each product is different in what it does best, but in most cases, you can create what you need in FileMaker more easily than you can in Access. FileMaker also "scales up" more simply than Access. There is no "server versin" of Access. When you need to upgrade to something with a server capability, you have to either design your database all over again or rely on a migration tool (such as what comes with SQL Server) to convert your files into a format suitable for the higher end database application--hoping that the resulting database will work with a reasonable level of efficiency.
Compare that to just taking your File created with Filemaker Pro and uploading it to FileMaker Server without having to make any modifications to the file...
The biggest difference between the two systems is that to get anything significant designed requires a basic Knowledge of the query language called SQL. This query language is very powerful and makes possible certain queries that FileMaker either can't do or can't do easily. But this language is also very cryptic to the new user and thus requires a fair amount of study to learn unless you are already familiar with how programming languages work.
FileMaker, out of the box, doesn't query tables with SQL. It uses more of a "query by example" method that is much more accessible to new users and makes setting up simple searches of your data very simple to do. But there's a point, as you attempt to produce more and more complex queries where SQL will out perform the way FileMaker works--so there is no simple way to say one product is better than the other.