Is there anything better than live recordings?

Studio recordings.

Live is the real thing, warts and all. I remember sitting in the balcony at Heinz hall in Pittsburgh and the acoustics were so bad I told my wife I'd rather be home listening to my stereo. First floor row H that's different. But I find the sound of a live symphony is more diffused with less pinpoint imaging than you can get with a recording sometimes, but that's less "real" in one sense.

"Is there ANYTHING better than live recordings"

That's a pretty open-ended question.  I'm hoping to pole vault on my 90th birthday.  That would be pretty hard to beat.

Related to the music, IMHO it depends on how important your engagement is with the performers vs the music itself as a "stand-a-lone" entity.  If you welcome a high degree of emotional interaction with the musicians (personality, intimacy, energy, great hair) your enjoyment may be enhanced by those factors.  It you tend to prioritze getting the music "right" then a meticulous rendering of the the performance may tip the scales in your favor.  That being said, if you combine those 2 factors, you may forgive a less than stellar performance/recording if the heart of the performers shines through.  So, doing the math, a performance/recording of a "4" combined with a stage presence of "9" may tip the scales in the favor of that recording vs a solid "8" studio recording.  A "10" plus "10" live performance would take extraterrestrial interfernce to produce a superior studio recording.

When a visual is introduced, the whole process gets more complicated.  A "3" performance + a "9" energy/presence + a "9.5" visual can produce a performance that can result in the most fun you can legally have at home.

Well, I don't know about all live recordings, but the back-to-back guitar solos on the Allman Brothers Live at Fillmore East in Stormy Monday are as good as any guitar solos get, and they were spontaneous.

Cheers!

I have to question anyone who thinks a live concert trumps a studio recording with regards to audio quality. It makes me think they haven't seen as many disappointing/meh live shows as a reference or are very selective about who they see in concert & want to listen to in a live recording. But I wouldn't go so far as to say live recordings trump studio recordings.

Ever listened to a Deadhead's bootleg cassette recording of a particular show? Terrible in every way. But that's my opinion. 

Most of my complaints about some live recordings tend to be poor quality micing for the vocals (they tend to go in and out as the artist moves on stage) and unequal mixing. Now there are some bands that record directly from the live mix and those can be fantastic as it's as much about the energy of the live show and variations to how the band plays certain songs. I've heard some great recordings in the last few decades but those tend to be video concert recordings.  

Conversely, Zepplin's concert film 'The Song Remains the Same' is great at capturing the live show and makes it, to my ears, a better experience.

For example, the live version of Wilco's 'California Stars' I heard in concert far surpassed the Mermaid Ave Lp version but that was because they stretched that into an epic encore version for a packed house in a historic theatre.

Conversely, I saw Black Rebel Motorcycle Club at the same theatre and it was one of the worst soundboard-mixed shows and loudest concerts I've seen. The distortion and mix were way beyond BRMC's intentions to the point that it made for unpleasant listening. 

I've also found that the venue plays a big part in how good a live recording can be. The Merriweather Post Pavilion in MD is a terrible place to see a live show - regardless of where you sit, it's just bad. Best outdoor venue? Red Rocks Amphitheater hands down. Club shows? That's hit or miss and very dependent on the in-house set-up.

All that said, I enjoy certain live recordings by my favorite artists but I'm very selective about which ones for the all the reasons I listed above. I have found that I really enjoy watching concerts via youtube when it's a professional production. Because then I get great audio and the energy of the live show. Which is why I go to concerts in the first place.