There are box players who also play concertina such as John Williams and Billy Mac..
I don’t think one preceeds the other.
As to the concertina types and the type of reed..
I am a former Jeffires owner.. 38 button… ( bought it for $300 US…correct $300 US)
I sold it to a fine player…
Since then I have played quite a few concertinas of all types…
While Jeffries still remains king with many I have played one Lachenal I much prefer.. and that owner traded a 38 button Jeffries for it ( and got back some cash)
Next I prefer the Button Box Morse Ceili.. and here I am certain I am in the minority..
I much prefer the accordion reed sound and resistance and modulation..
But that is from a box players perspective.
Assuming I had the cash to buy any concertina now available.. I would still buy the Button Box Ceili or perhaps a
Geuns or an Edgely, again because of the reed sound and playability.
A Button Box Ceili runs about $1950 new
a two row Button Accordion in that price range would be the Saltarelle Bouebe, and from personal experience it is no where near the quality of the Button Box Ceili.. in design, materials fit or finish
You would have to go up to a Castagnari Dinn II to get something on the order of the Ceili and that would set you back a considerably higher sum
I like the “idea” of a concertina.. small portable somewhat chromatic and dare I say “cute” ( gag)
however in actuality I am with some others that dont get the wee bit on the knee thing
For hoots and the concertina sound with huevos try a Castagnari Lilly in a C#/D or a B/C under $2K and at least you get some bass buttons and Castagnari quality… while not yet in the 'manly" category at least it is a serious handful
Pick something decent and just get on with it… concertina or the box
PS I don’t care for the standard concertina C/G pitched units… I prefer lower pitched G/D or even the baritone C/G…