Irish-style players have tended to prefer the 30-button configuration. It's lighter, less expensive (for a new one, at least) and more commonly encountered, and its range and layout are (as you surely know, since you play one) perfectly adequate to the Irish dance repertoire.
Personally I appreciate the alternative fingerings that additional buttons make possible: on a 40-button instrument I have access to many more chord voicings, and I often have the option of playing melodies in a more legato style--something akin to the phrasing that comes more naturally to an English or duet concertina--by eliminating many bellows reversals. But complex chording doesn't figure much in Irish-style playing, and I have to be on guard against playing *too* smoothly, and losing the distinctive bounce that's such an important feature of the style. If I only played Irish music, I might well prefer fewer buttons.
As for Wheatstone vs. Jeffries, there are contrasts of internal construction (orientation of the reed pans, etc.), but the most obvious difference is the arrangement of the accidental row. Here's a site illustrating the layouts:http://www.concertin...ges/finger3.htm
(My 40-button Wheatstone follows this arrangement pretty closely; my older Lachenal departs from it in a few places, most usefully by incorporating a draw E in place of the low C# on the left hand accidental row.)
Many Irish-style players prefer the Jeffries system, mainly because it supplies the C# on the right hand accidental row in both directions, whereas a 30-button Wheatstone system has it only on the push, which can be confining. But the thing to note here is that a Wheatstone-type instrument with additional buttons will give you at least one C# on the draw, eliminating the problem. It's only on 30-button boxes that it's a concern--and anyway, countless Irish players have used the Wheatstone system; it's not a hugely challenging adjustment.
As for me, I like the logic of the Wheatstone layout, even on a 30-button box. Among other considerations, I'd be lost without the push A on the right hand accidental row. Add a draw C# or two, and I don't think there's a downside.
Hope this helps!
Edited by Bob Michel, 27 July 2015 - 11:31 AM.