It's not as much a question of which of the two will be understood by more people, as it is a question of how to implement each one.
You know how you make buttons look like buttons? Excluding the latest "flat design" fad, pretty much all buttons have a gradient, some drop shadow, or at least a border on one or more sides. This is not just to make them stand out as a "there's action here" element on a page. The main reason, is so that it mimics real life's buttons, which everyone knows how to use.
My point is, even with something as elementary as buttons, we try and give people hints on how to use it.
A few examples
Whatever you end up implementing, make sure you explain to a user how it works. Here are a few example methods off the top of the head;
- A line or paragraph of text explaining how to sort the items; "Click and drag the icons next to each item to change their order!" that's highlighted at the top of the page.
- A click & drag indicating icon supported by a tag that pops up on hover saying "click and hold to drag and drop".
- A big button saying "Order" or "Sort items" or something similar, that transforms all elements in (un-editable) drag & drop elements.
Whichever you end up using, or whatever you come up with, keep in mind that it's about explaining what's going to happen. Whether that be by visual stimulants, text, or a talking paperclip at the bottom of the screen (don't!) - hold their hands and explain the process.