Are there parallels to Asterisk AMI and AGI in FreeSWITCH?

These are good questions. I just wanted to add a few things to what @dkwiebe said (which is correct, BTW).

The AMI equivalent in FreeSWITCH is the event socket. (Technically it's not the "Event Socket Library" or ESL, which is an abstraction layer for writing programs that use the event socket. I just wanted to make that distinction.) In fact, the FreeSWITCH equivalent of "asterisk -r" is actually an ESL-based program called "fs_cli" - short for FreeSWITCH Command Line Interface. The fs_cli program is a great example of what you can accomplish with ESL.

Also, there is no reason that you cannot use an ESL program to do many of the things that can be done with AGI scripts. The ESL "connection object" can "lock on" to a single call leg and control it. There are examples on the wiki and the forthcoming FreeSWITCH Cookbook will have some recipes on the subject. (Full disclosure: I am a co-author of the FreeSWITCH Cookbook.)

Another ESL-related method of controlling calls like AGI is with the fs_ivrd daemon. It's less commonly used than ESL but is a nice option for AGI-like scripting. See this wiki page for more details.

Lastly, I would like to mention that Lua is a great choice for doing scripting/logic/etc. in call control. It is simple, light, and easy to learn. In the lab we've seen a few thousand concurrent Lua-controlled calls on an 8-core machine. Lua works even in some very demanding environments.

Feel free to join #freeswitch on irc.freenode.net to discuss your questions with the FreeSWITCH community.

There's a page on the FreeSWITCH wiki addressing most of these "Asterisk to FreeSWITCH" questions: Rosetta Stone.

AGI are for scripts used durring a call (i.e. called from dialplan durrign dialplan execution). Scripts that listen to the AMI and wait for events are standalone. While that latter, can, technically, do the former's job as well, you are much better off keeping them separate.