I would certainly recommend it if it is better, but how much better is it really? I hear they both work in the same way and produce almost identical results. Difficult to justify the USD$55 it costs when a similar/better alternative is free.
I can only talk about MY experience and each website can be a diferent case. I don't tried the last version of IRCmaxell. I installed this component more or less 3 months ago in a dev site and after that I tested the component from joomlatwork.com
The result was really better with the last one! Nothing compare. Few months ago, IRCmaxell was using SQL queries but with Joomla performance booster it was possible to base the cache on cookies. So the cache was very faster since file based and not SQL based.
Another point for me is VERY important: support! Here at RT the support offered by the community is amazing, at joomlatwork.com the support by developper is simply the better I ever seen in the joomla world (and I purchased a loooooooot of commercial components/modules/mambots)... yes, I must tell the admiration I have for support provided by Richard! He resolved the issue I had with other components and custom modules (like CB) in less than 24h and always answered my questions (before and after purchase). Moreover, joomlatwork refund you if the component does not work like you want. There is no risk.
However, I don't know about the support at IRCmaxell and about the last version.
In my case Joomla performance booster work better and I can have an incredible support.