As a student in a rural area that has some larger cities (and hospitals) fairly close by, I've gotten a chance to use both during my clinical rotations.
Being a computer nerd, perhaps I'm a bit biased, but I greatly prefer computer charting. I can type much faster, it's a lot more legible (My handwriting is atrocious), and as a student who doesn't always remember to include everything, the ability to just go up and type in what you forgot to include is incredible (As in, I'm charting a head to toe, in that order, and I forget to include the apical, lung sounds, or bowel sounds. Instead of having to write those at the end, I can just scroll up to where it should be and include it. It's less messy.) Best of all, there's BACKSPACE! If I accidentally misspell a word, I can erase it and retype it, instead of putting a line through it.
Not to mention, if the computer has internet access and you're completely unsure how to spell a word, Google is only a click away (I make frequent use of that).
Also, going back to forgetting something while charting, at least one hospital I've been to has had canned text with their charting. You just fill in the blanks and add what you need as you go. It makes it clean and easy. Granted, it'd be easy to get lazy and just plow through it without adding anything relevant to the patient, other than what is presented to you on the screen, but if I ever get that way, then I'm not doing my job.