Different methods of shuffling cards relevant? YES Do Glorps, as players, prefer the method which is more effective YES and Morps, as collectors, prefer the method which results in less damage to cards? YES
I'm thinking about two real methods, but have difficulty to name or describe them accurately. One involves dividing the deck into two halves and mixing them up with a single hands movement - it's effective, but it's said to damage the cards. The other one, much less effective, involves getting the deck of cards from one hand to another with a series of repeatable movements, mixing the cards in between.
That looks about wrapped up.
As a player of a collectible card game (CCG) called Magic the Gathering (MtG) and a lot of other card games and board games, I find myself doing a lot of shuffling of cards. Since serious MtG players (Morps) are often playing with decks worth hundreds of dollars, if not much more, they want to keep their cards in as good condition as possible which has led to the rise of some interesting shuffling methods...with questionable effectiveness. The most effective of which is basically grabbing two halves of your deck in a sort of fan formation and sliding the two halves together. Statistically speaking, this might truly randomize your deck after an astronomical number of shuffles. The less effective methods include "randomly" putting your deck in N piles one card at a time and then stacking the piles together or smushing your cards together in a big pile and then restacking them.
If you were to sit down at a poker table or at a casino with some serious gamblers (Glorps) and did that sort of shuffle on your deck of standard playing cards, someone would probably call you out on it and accuse you of cheating or stacking the deck. You would be expected to do something like a riffle shuffle which, when done correctly, randomizes in a very low number of shuffles (I believe around seven or so).
And so, if you shuffled like a Glorp at a Morp table, you risk damaging the expensive cards. If you shuffled like a Morp at a Glorp table, you're not randomizing properly and might be accused of cheating when people are betting money on the game.
Personally, I shuffle like a Glorp because I think my MtG deck should be properly randomized when I play. Plus, the "damage" that people usually quote for the method is giving the cards a very slight backwards bend which seems to help with picking up and moving cards around the table (because the center of the card sits a very slight bit off the table). Besides, the damage happens to my cards in my deck and the damage should be uniform among the cards. And those cards are probably never going to be traded to other people. But, if I am borrowing a deck or handling someone else's expensive cards or playing in a draft, I will often try the other shuffling methods or just let someone else do it for me.