Foreword. With this question, my motive was to poke at the chord symbol naming system, to learn more of its properties. I've been intrigued by the idea of learning what the traditional "stack of thirds" and "seven notes per octave" model of harmony naturally lends itself to, and when we start to feel like being on uncharted territory if that model is all we know. The diminished scale has eight notes per octave... and then there are things like quartal chords, for which we might find approximately equivalent counterparts in the "stack of thirds" world, but a lot gets lost in translation. And the Hendrix chord has two different thirds at the same time! (But according to its commonly used modeling, the other one is modeled not as a third, but as an augmented second ... ) It's unfortunate that the question ended up being seen as "what's the right name for the Hendrix chord". My initial starting point was assuming that the common name for the chord was "correct" ... but I've since refined my opinion. Which was, I guess, what I hoped to achieve. Thanks everyone for spending time and writing answers. It's a very tiny group of people out there who care about things like this.
The so-called Jimi Hendrix chord is commonly called E7(♯9) or E7♯9, implying that it "is" a major chord, but with a sharpened ninth added. Not caring about the chord already having a commonly used name, and the voicing of notes in the Hendrix chord having the third lower than the ♯9, is there some harmonic aspect about it that would be misrepresented by thinking about is as a weird or surprising voicing of Em7(♭11)?
To me the Henrdix chord sounds like a minor chord just as much as a major chord, so implying that it's somehow innately more major feels questionable. Bluesy harmony is IMO a mixture between minor and major anyway. "♭11" is not a very easily understandable way to say "works kind of like a major third", but then again, "♯9" is a bad way to say "works like a minor third" as well.
I guess I'm really asking about voicings and chord naming. (EDIT: Bzzzt! No, that was just my first idea before getting a better understanding from the many answers) If we expand the idea of "E7(♯9)" outside the one particular Jimi Hendrix voicing of it, or think of it as "the set of all possible voicings for E7(♯9)" - wouldn't it be enharmonically equivalent to "the set of all possible voicings for Em7(♭11)". (EDIT after getting wiser: well yes maybe, but the set of sounding notes is not the only aspect to consider)
To explain my argument of the chord's not being self-evidently more major than minor, here are two example melodies:
YMMV, but to my ear, the one with the minor-key melody conforms to the backing chord slightly better than the major-key melody.