I like this thread!
I use a variation of techniques driven by intuition.
A good method that I just recently got to try out is one that I read in my one of my tarot books (can not recall which at the moment). I just moved and I have a new roommate that just moved here from the UK who wanted me to read for her. I felt good energy from her and thought she must be more 'open' then she seems (very reserved) but I still could not get a clear enough read on here as to what deck should be used to best speak to her energy. So I tried out the method of pulling the High Priestess Card from each deck (it would be the Magus/Magician for a male) and placing the card on its deck and have my querent choose which High Priestess card she felt most connected to. She chose the one from my Legacy of the Divine Tarot deck and added the comment, "doesn't EVERYONE choose her?!", which left myself (as well as her) feeling confident that she was about to get a very connected reading (which she said she did)!
At other times I find it very easy to pinpoint what deck a client would enjoy being used (i.e. my friends that would get excited about 'nerdery' LOVE my Steampunk Tarot, while my more world-traveled friends would relate to my World Spirit Tarot better).
However, what a person LIKES or PREFERS is not always what is APPROPRIATE for a particular reading to speak. Case in point, my lil sister. She is an extremely strong-willed and opinionated young woman and it has actually really advanced my reading skills reading for her. Yet, we went through a time of butting heads over what decks I would use to read for her because she is a 'backseat reader' and would contradict me or simply complain about how she did not RELATE to the deck or that she thought the deck was illustrated poorly and it bothered her, etc. Granted I had spoiled her by finding the perfect reading deck for her as a gift (Wizard's Tarot). We had to solve her stubborn blockage for a while by having me use HER Wizard's deck when I read for her so that she could relax (even when I could feel that other decks where trying to speak to her. The end result is that she now trusts me with readings, opens up regularly and calls me from out of state to do over-the-phone consultations for her. I even just did a Madame Endora's Oracle reading for her that just ripped open some secrets to a situation that she was able to confirm..
That leads me back to the intuition thing. Sometimes I feel that a deck can not 'get its words out' by itself and needs a 'friend deck' to help 'back it up'. As in the above case with the Oracle deck I then took my WST deck and read over the same situation and got even MORE insights!!
THAT leads me to the fact that I feel that certain decks seem to 'get along' better and others just do not. I do not think this is an absolute (i.e. ALL Llewellyn decks can not get along with ALL such and such decks, etc.) However, myself (as well as my sister) have noticed that certain decks seem to want to play the Hermit whilst others are very much 3 of Cups-ing it!
So that makes it just as important which decks I choose NOT to use as which ones I do. My Llewellyn deck is my first deck that I bought but for a while it did not seem to want to be put with my other decks. Now its relaxed a bit and is stored with the others but it just reads in a very harsh uninviting way. Before buying it, I had used llewellyn.com to do many accurate readings with it and loved it -but something is just off with the deck, i think. My toddler niece is supremely metaphysical and likes to observe my tarot decks but that deck she set hands to, found its three of swords and CRUMPLED it! So yes, deciding which ones are out of the running is a worthy point to me as well.
Another things that helps me choose is the overall message of a particular deck itself. For instance, Legacy of the Divine Tarot is very much a long-term view, higher consciousness deck -and that is exactly the way it reads most of the time. Even before I read the companion book its readings took a more vast nature. Steampunk Tarot is very much a quirky solver that deals with the inner mechanisms of a situation and challenges people to find bridges over different viewpoints and energies. My World Spirit Tarot is somewhere in between being both good with the day-to-day living and the longer term, broader views which, again is the energy of the deck's creation itself. That is the deck that is the easiest to use in everyday random situations and the one that I carry on me always