Many people argue that the original version is superior, but I don't know.
I've had the first version on boot for years and it was cool to hear so countrified and raw. Loved it!
It's a matter of preference since they're both sublime.
Explain your choice. Here's mine.

I still keep going back to the Exile version, what I call the Nicky take. That piano is probably the first thing of Exile that hit me, just really hit me.
Don Was prefers the original and told the Stones they used the wrong version, but the Stones were in a different groove by 72. While I love the original's grit, it sounds like it belongs on BB or LIB, that period where the Stones were experimenting with different styles. To me, its closer to Let it Bleed than say, Shine a Light or Let it Loose. It fits on Exile.
Also, the first version has Mick doing his best country twang, which at that point, was still very exxagerated. I loved Keith's guitar in this one, but it makes it sound more sluggish, more druggy, as does Jagger's vocal. Gimme lil drannnk....
The Exile version has Jagger singing a more straight vocal, without the exxagerations. Like he's sober and means it, rather than stoned.
And of course, Nicky Hopkins piano - its just sublime, and to me, it carries the song all the way through...he's possessed here and its beautiful.
I would say the difference is that in the first version, the Stones sound like they're in the studio, its 4a.m. and they're stoned. On Exile, it sounds like they're in church.
That's the difference between great and sublime.

The alt take is fantastic, but I can totally see why they put the original Exile version on the album: it's more soulful and fits in better. But I guess I feel that way because I've been hearing it and loving it for 20 years..