Without borders in my opinion. They wouldn't do much other than outline what's already been outlined by the background/foreground color differences. Unless I am mistaking what you mean by "with or without borders."

You can compare the pictures there. I took two screenshots of the same page with and without borders. The borders are the rounded boxes around each section and the sidebar.

Ah, saw them the other day then. I like it, gives variation, rather than bland white everywhere.

I'm leaning toward no borders now. Twitter uses them, but I sometimes feel like they could go without. Imgur uses them, but they could probably go without too. I like how StackOverflow, Dribbble and GitHub do it. Very simple.

Tbh, they look nice. Doesn't look so blahh.

I'm considering a very subtle border with a very subtle background color.

I ended up keeping the borders, but they're very faint due to the subtle different in foreground and background colors.

If all else fails, go for subtle!