To be honest, it depends on the club and the individual.
Personally I would stick to the club, so that you can have continuity of training especially about times and dates. Airlines often will call people at the last minute and you may find yourself left in the lurch.
There are all the usual boring reasons as to why most instructors need to work through a club; insurance, CAA approval (has he registered himself as an RF?) A good full time instructor is usually better overall than a part timer, simply as they are more current, especially when it comes to rules and reg's specific to training.
Airline guy's are good in the respect that they know the standard and, most importantly, the mindset required for the commercial world.
Have the occasional sortie with this chap, but leave the bread and butter teaching to a good school.