I cannot choose one over the other because I did not attend any of these shows. I was too young then and Madonna never bothered returning to Southamerica until her signing at Live Nation. However, I can point out some facts about them.
The Re-Invention World Tour
The Re-invention Tour was a show she needed to do in order to reconnect with older audiences, especially after the Drowned World Tour which focused mainly on new material and left a lot fans unsatisfied. It's true everybody was still drooling over the ROL and Music eras and she was regularly played on the radio up to the announcement of the American Life album, remix edits included. It wasn't until the controversial flop surrounding AL that everything had to change. She had to swallow her pride and retract from saying she would never play Material Girl or Vogue ever again! The tour was indeed promoted as a Greatest Hits show.
It was great to see her choose at least one song from each one of her albums, omitting the Who's That Girl OST only. The setlist was excellently balanced: 8 songs from the 80s, 8 songs from the 90s, and 7 songs from the 2000s plus a cover.
I do agree some of her costumes were not as awe inspiring as the rest we have seen in other tours but who doesn't like this one and its golden version? It's Madonna 100% and it's now really memorable!
Her make-up was also on point. She was fabulously rejuvenated during this tour.
I think the tour suffered a lot from Madonna's negligence (and her management as well) in that they never gave us a proper DVD with the complete concert. We only got the documentary and some live highlights to remember it! I do think not touring new countries also affected its reputation to some degree. She didn't got to Spain or Italy which was shocking at the time. She didn't visit Japan either.
The Confessions Tour
With this tour Madonna gave us an enhanced experience of what we had already seen in 2005 during the gigs she gave to promote Confessions on a Dance Floor. It was basically a much bigger spectacle with more ideas put on the table (equestrian and bedouin themes). We had already seen the disco ball in the Girlie Show, the Catholic imagery during the Blond Ambition tour except that the crucifixion was just more over the top. Madonna playing the electric guitar had already become a trend since the Drowned World Tour. So it wasn't 100% innovative from her as she just repeated the same old formula.
The greatest thing about it was that she had a really strong record (taking inspiration from ABBA, the Pet Shop Boys, Donna Summer and Goldfrapp) which was also able to attract a new generation of fans. Madonna at 48 proved she still got it.
My favourite thing about this tour is that she collaborated with Gaultier again. He always brings the best in her! She looked flawless, younger than ever and quite fit. Wish she had kept him for the Sticky & Sweet tour which was distasteful in this department.
What I did find weak about the show at the time was the interludes. Almost 10 minutes of Live to Tell and Sorry used twice. Wasn't it a bit too much? The most ridiculous thing was to find out that they were included on the live CD instead of more interesting selections that could have been used... whatever.
Forgotten classics that returned to her setlists: Like a Virgin and Lucky Star while Holiday got a well deserved rest!
Apart from the financial success of the tour which visited more countries around the world, we did get a DVD intelligently edited by Mr Akerlund. That is for sure one of her best filmed shows and the general public love it til this day.
For me they are equally A-M-A-Z-I-N-G