To understand Airasia's competition (Why Airasia? Because I own its shares and also MAS is not listed), one has to know where MAS is heading. The below video shows that MAS is not going to fight on price anymore as opposed to previously. This is bad for me as a consumer but good for me as an investor. I remember I took a lot of Firefly flights between Penang - Subang at RM39 - RM45. Those tickets are not available anymore despite fuel price still cheaper (than 2 years ago).
MAS is now acting just like a full-fledged airline - they should as they do sometimes have a captive market - i.e. government employees (Yes, Govt employees usually take MAS as compared to Airasia). Additionally, since MAS has its own plan of getting to profitability (presuming it is going into the IPO market by 2019), it will have to be more discipline in pricing its tickets. It will be much less getting into price war - which is good for the airlines generally. Yes, MAS is also much tighter in terms of its costs structure - but generally from the interview you would notice that Airasia has a much earlier headstart as it was able to have better and proper planning against MAS which was struggling for a long while.
Also, I would like to highlight although people would have thought that Malindo is a major competitor to Airasia, it is not actually. Malindo gets its planes from Batik Air (owned by LionAir) which is a full fledged airline in Indonesia. You would have noticed that Malindo sells business class seats (and has IPTV screen) compared to Airasia which does not. Hence the costs and pricing structure are different. This makes what Tony Fernandes says i.e. Malindo is more of a competitor to MAS than Airasia is somewhat true.