A lot of it is to do with the quality of the work - an organ voiced by Arthur Harrison would be as good as anything available at the time and better than most. Also, Harrison was influenced by George Dixon, who was clever at devising schemes which got the most out of what was available and avoided redundancy. Thus, the Harrison/Dixon team could produce a small organ which was complete and versatile, whereas others were content to provide a selection of mostly soft stops which the local cathedral organist would use most often to accompany a choral service, plus a big diapason to lead the hymns.
Father Willis's "Model" organs were similarly clever, and an influence on Dixon. The mobile "Stainer Organ" in St. Paul's Cathedral is the best known example (Mander added a Great Mixture) and is recorded as having been capable of leading a full congregation when the big organ was out of action as well as having been mistaken for its larger brother on many occasions.
Great: Open Diapason, Lieblich Gedact, Principal, Fifteenth
Swell Open Diapason, Gemshorn, Cornopean
There are other, similar jobs around the country. I can think, offhand, of Dennington and Groton in Suffolk, the Song School at St. Mary's Cathedral, Edinburgh, Great Horkesley, Foxearth and Stapleford Tawney in Essex (these two a bit bigger), Wolferton in Norfolk.
Other builders were less imaginative at getting the most out of a small number of stops. Here's Binns at Stromness Parish Church, Orkney:
Great: Open Diapason, Rohr Flute, Dulciana, Principal
Swell: Geigen Principal 8, Gedact, Viole d'Orchestre, Vox Angeilca, Salicet
You need a few more stops to get a really interesting Binns. The same goes for Lewis - here's what he did at Woolverstone, Suffolk:
Great: Open Diapason, Lieblich gedact, Salicional, Octave
Swell: Geigen Principal 8, Rohr Flute, Geigen Principal 4, Horn
Pedal: Sub Bass
or Dundrum, Co. Down:
Great: Open Diapason, Lieblich Gedact, Dulciana, Flute Harmonique 4
Swell: Geigen Principal, Rohr Flute, Viole de Gambe, Voix Celeste (all 8')
Pedal: Sub Bass
Small Bevingtons can be rewarding, especially if they run to a mixture, but at other times, especially later instruments, they can be deathly dull - like Little Horkesley, Essex (installed second-hand when the church was rebuilt after a direct hit from a land-mine in World War II):
Great: Open Diapason, Dulciana, Lieblich Flute 4
Swell: Stopped Diapason, Cor Anglais, Principal, Sub Octave Coupler (the Cor Anglais is a gamba, as usual with Bevington)
And so on. Sometimes, these gormless-looking instruments sound rather good and much better than one would expect, like the Hope-Jones that used to be in St. Mary's RC Church, Croydon, where the only upperwork was a 4' Lieblich Flute in the Swell, although there were a lot of octave couplers (and a 16' Rohr Bourdon on the Great!).
Norman & Beard built dozens of small organs in East Anglia, which are generally pleasant and a cut above the rest, although maybe not over-exciting. They each seem to have a particular character.
Acoustics can make a difference, too, but some of those little Harrisons were in fairly dead buildings.
I think it's the master touch that gives the magic.