Like the G Treble Flute, the E-Flat Soprano Flute is pitched midway between the C Flute and the Piccolo. It is the only member of the modern flute family not pitched in either C or G. The pitch of E-flat is a relic of a time when bands sometimes used a small flute to replace the small E-flat Clarinet.
Jazz saxophone plays sometimes will use this instrument due to its key being the same as the Alto and Baritone Saxophones. In this same regards, some manufactures will make a B-flat “Tenor” Flute* pitched a second below the C Flute (and a minor third above the Alto!) for use in jazz.
The best of my research leads me to believe that this flute is no longer being manufactured by any companies, so any instruments will be older (though, by no means unserviceable). I would generally advise against the use of this instrument. Being pitched only a minor third above the C Flute, it does not provide much of a range difference, only four or five notes higher, and those are questionable in response. The sound is also fairly similar to the C Flute. If, however, you find yourself having this instrument available, then its technique will be the same as the C Flute.
Were I to have to choose between the G Treble and the E-flat Soprano, I would always choose the G Treble.
[*Flutes pitched in either B-flat or A below the C Flute are more properly known as Flutes d’Amore.]
2 E-flat Flutes with a C Flute playing a Scottish melody.