I used to do this when I can find a 40% difference or more in price on an item which isn't too common.This is probably best done with things that are popular or trending. Right now you can find new toys for something like $19.99 on Amazon and sell on eBay for $26.95 which is only a $2.46 profit. In order to make this "worth my while" I would have to make at least $200 a day, so I would need something like $1630 set aside for a days' worth of transactions. If I were just starting off I might consider it, but the time between listing an item on eBay for the lowest competing price vs the current price of the same item on Amazon might change.
You could make a list of a couple hundred items on Amazon that sell for 20% cheaper on eBay, and when it sells on eBay, you buy it on Amazon and have it sent to that persons' address. I wouldn't recommend doing this if you are not a top rated seller because that discount can really save you a lot of money if you are processing so many transactions a day. (So instead of $2.46 in profit from the item I listed above, you would make 3.05. 80 transactions a day, that could be an extra $47)