Technical question

The 301 would be best. A lot of people are misinformed on this
and think that the sky will fall if you don't do anything. It won't
It's really no big deal. Google will (maybe) think they are 2
different sites, but in the real world, not really. Google picks one
or the other. In your case, it's not really a big deal. But like I said,
you will get a lot of crazy people who think google will think
vile thoughts and take action. They won't. It's common. This is
not 1995. People know that whether they type the www or not,
it's the same site. So does google. The one they choose to display
will be the one they think gets top billing. Since you already rank
for the www version, better to do a 301 from the non www to the
www, then it won't matter anyway which site you build links to.

It's not as a grave situation like so many people have been led to
believe.

In fact, if you build all links to same version, no problem anyway.
And if you don't, it's not really that important.

There are so many other things to worry about, I don't know why
this topic seems to be batted around so often.

You can put your preferred version in a sitemap as well.

Since we are only talking about 2 different versions, it's not
that big of a deal. If you have a dozen ways of getting there,
it may be a problem by diluting the links if you built links for
all versions.

Be consistent in link building and you have no problem.

Paul

Well, like paulgl wrote, just do 301 redirect. That should preserve most of the backlink link juice. And it's a good thing to have the 301 redirect under all circumstances to ensure other incorrect backlinks give you the full backlink juice