I've blogged a bit about how paper scripts are becoming obsolete for readers. I personally can't justify the expense or eco-unfriendliness of printing out scripts (and it doesn't help that my printer, which I bought because it's supposed to print two sides at once, crunches up paper in endless paper jams). I read almost all scripts on my laptop screen, which does kind of suck, but since I have to write notes (and often synopses) on scripts, it's most convenient for me to read the script while also keeping a Word document open. If I read a script on paper, I'll have to write notes with a pen and then transcribe them later, which seems extra time-consuming.
I do own a Kindle DX, which is perfect for simultaneously reading and browning oneself on a rooftop, but it doesn't allow me to make notes; I can only bookmark pages, which isn't all that helpful when I have to write extensive coverage. If I'm simply reading scripts for pleasure and don't need to write notes, the Kindle DX is great (the DX is larger than the original Kindle, and makes PDF scripts the perfect size for reading), but 95% of my reading is for work. On iPads (and Kindle Fires, probably) you can use apps to annotate documents, but I need to send official typed documents, not drafts with annotations. (Plus, the whole sunlight thing.) I hope to someday get a tablet for watching TV & movies while I'm at the gym, but that's a whole other multitasking conundrum.
I can't really speak to contests like the Austin Film Festival - I would think that they scan all the submissions in to have electronic records, so readers might read them electronically anyway (or, conversely, print out electronic submissions).
Ultimately, the "experience" of reading doesn't really cross my mind...I read hundreds of pages each week and need to write notes quickly!