Dyalog uses non ASCII symbols which are really cool to me and make the primitives very easy to learn. Check out tryapl.org to get a feel for it. You can also download a trial version and there is a free book. They have decent library support and full .NET support too as well as easy parsing for CSV, JSON, XML...etc. They have Dyalog APL notebooks, database access, multiplatform support, parallel and tacit features...etc. If it wasn't $1k a year for a license (honestly pretty reasonable) I'd use it pretty often. It just feels like they love their product and support it from the annual coding competitions, monthly webinars...etc.

J uses ASCII symbols and has a small community of very intelligent users that are stats smart, software smart, math smart...etc. It has great bindings to Lapack, built in graphs (well Dyalog does too) and tutorials called labs. The community is much smaller though and it doesn't have any parallel primitives. J is free to use, but the Jd columnar database is commercial, but very reasonably priced.

Honestly, both are awesome, fun, powerful, and plain cool.

Among other things, Dyalog now employs Roger Hui, one of principal creators of J, so Dyalog APL features are using full knowledge of J. Arthur Whitney's, the author of K, wrote the first implementation of J. So it's a small world...