The best way to compare them is just to try them out. Fortunately, the UK intel group GCHQ came out last year with accurate simulators for Enigma, Typex and Bombe (the Enigma-breaker).

https://github.com/gchq/CyberChef/wiki/Enigma,-the-Bombe,-and-Typex

The other thing I'd recommend looking into is the fact Engima was broken in a complete sense, while Typex was not, even though the Germans managed to decipher some Typex messages. See Dermot Turing's recent (excellent) paper The Typex Scare of 1943: How Well Did the British React to a Cypher-Security Scare?

http://www.ep.liu.se/ecp/article.asp?article=004&issue=158&volume=#

You also may find (although this is homework so I'm not going into detail) that the extra rotors weren't really the reason why the British machine was more secure.

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