There is no real advantage or disadvantage. It may be very slightly faster than using pairs, but micro-optimizations are never good justifications.

This is more or less the definition of pairs:

function pairs(t)
    return next, t
end

So it's pretty much the same thing to use next, t and pairs(t).

What is next?

next is the interesting magic that makes it possible to traverse a table.

You give it a table and a key, and it tells you a next key to look at.

local tab = {apple = 1, banana = 2, orange = 3, melon = 4, tangerine = 5}

print(next(tab)) -- melon, 4
print(next(tab, "melon")) -- banana, 2
print(next(tab, "banana")) -- apple, 1
print(next(tab, "apple")) -- tangerine, 5
print(next(tab, "tangerine")) -- orange, 3
print(next(tab, "orange") -- nil

note: next (and pairs since it relies on next) does not return things in any particular order. If you keep re-running the above script, you're probably going to get different answers.

How does next work?

Tables in Lua are implemented as Hashtables.

This means they are blocks of memory that get labeled with keys (in random order) and containing values.

Since it's just a block of memory, guaranteed to be relatively packed with values, it's fairly easy to do what next does, at least in C.

It is not possible to implement next in Lua.

Which do I use?

Some will say it's better to use next because that's what's really happening underneath.

Some¹ will say it's better to use pairs because it's clearer what you mean.

As with all style choices, the most important thing is to be consistent.