Well for me, for the most part, the basic meanings of the cards doesn't change very much from deck to deck. But what does change is how they look and "feel" in a reading. Sometimes it isn't the meaning that changes so much as the "flavor" of the interpretation - meaning how it might be presented to me or rather how I deliver it to the querent. Other times the image might lead my intuition to a rather different interpretation all together.
So, for example, if the 8 of Swords in a deck shows the chains or ropes binding the person as being tightly wound around them, I might interpret that as indicating they may be trapped by something more beyond their control. Whereas if the ropes are loosely draped around them, I might think it is more self-imposed.
Or, with one of my favorite cards of the Tarot, The Chariot, the presence or absence of reigns (or other means of physical control) can change they way I see the card.
I think I really started reading more intuitively this way when I started learning the
Röhrig Tarot. I'd learned on the RWS, so the Röhrig was a real change for me. Opened up a lot of new ways of looking at the cards. I now have a lot of decks and try to use them all. And every one of them can lead my mind in new directions when I read with them. The
Necronomicon Tarot is another one that has led me to some different, non-standard interpretations of the cards.
I love using different decks. If you have other decks that you want to work with, I highly recommend the
Deck of The Week threads (the link is to the current one). They give you some incentive to try your different decks, as well as maybe getting some good information on the decks other folks are using.