largest language class for which inclusion is decidable
Converted from comment: language inclusion is decidable for very simple deterministic pushdown automata ("On the Inclusion Problem for Very Simple Deterministic Pushdown Automata (1999)" by E. Makinen, 1999) 
and a restricted version of timed finite state machine ("On the Language Inclusion Problem for Timed Automata: Closing a Decidability Gap" by J. Ouaknine and J. Worrell, 2004).