I have worked doing customer service for several different companies. Some have paid me by check and some have paid me by direct deposit. The current company I work for does payments by direct deposit and I have to say I have been much more satisfied with it. You don't have to wait for the mail or worry that your check won't be on time. Normally, as early as 8am on my payday my paycheck is already right there waiting for me. Which method of payment would you prefer?
I think payment electronically (or billing) is a preferred method so long as both parties are willing to trace the payment should it not get from one party to the other. While most mail goes fine, without paying for delivery confirmation or real time tracking there is no way to find a check that doesn't get delivered when it should, or at all.
Direct deposit of course, then you don't have to worry that a check given to you will bounce! Not only that, some bank accounts hold deposited checks until they clear, meaning you have to wait for your money.
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I'm not sure that I think that either is particularly safe-both have their risks. I've had direct deposits go missing, only to turn up at another branch of the company I worked for. I've had cheques sent to addresses I haven't lived at for years.
They both have problems, but direct deposit is definitely more convenient.