No.

I don’t know where he gets his information from, if it has happened to him then it would need investigation to confirm one way or another, what other security based applications were installed, not to mention when it happened and what avast version was being used.

The current build of avast 6.0.1289 is very stable and that include the behavior shield.

It rather depends on what comodo product you are going to install (make sure you don’t install the AV element), just the firewall and defence+ should be fine, but might increase resource use. So depending on your system spec (CPU, ARM, etc. ?) it could slow your system.