Disclaimer: I am not an attorney at law, nor is this legal advice, especially in your jurisdiction.

With programs licensed under the GPL and the Artistic license, you are free to choose one to follow. You do not have to follow both. (You are also free to make other arrangements with the copyright holder, if you can.)

Under the GPL:

• You must make the sources of your product available to anyone to whom you distribute your product.
• Linking to a GPLd application still falls under these rules.
• It is *probably* okay not to distribute sources executed only on your server, as the output of a GPLd program is generally not also GPLd. This is a point of contention, however, and will likely be addressed in GPL v3.
• In general, only the copyright holder can pursue legal action against someone violating the license. Specific laws in your jurisdiction may apply.
• If you modify the program, you only have rights to your modifications, not the original version.

Under the Artistic License:

• You are not required to provide your modified sources to people to whom you distribute your modified version. You must provide documentation that describes your changes in detail, though, and you must rename any modified applications. You must also provide instructions on how to obtain the original version.
• Linking to libraries or packages under the Artistic License does not require your application to use the Artistic License.
• The output of a program under the Artistic License does not fall under the license.
• Again, it's probably only the copyright holder who can pursue license violations.
• If you modify the program, you only have rights to your modifications, not the original version.

In either case, you do not have a right to the source of an application from a user or company if the application has not been distributed to you. (That sentences parses poorly.)