written or verbal offer

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Does a verbal offer carry the same weight that a written offer does? Is it seen the same way?
I wanted to put an offer on a house today, and the agent said she'd like to make it a verbal offer. I asked her that question and she said there was no difference. She just had to let the other guy know it is a legitimate offer.

Is that right, or should I have gone with a written offer?
Thanks.