If we're talking about the playing of composed music, the potential of each instrument is determined to some extent by the literature written for it. Perhaps the last point is where the cello has the edge over the English concertina?
Here's what you can do to change the sound of a single note/sound on the cello/violin:
1. Press harder/gently with the bow to change the volume
2. Play nearer/further from the bridge to change the tone
3. Move the bow faster/slower to change the tone
4. Make the pitch slightly (or very) sharper/flatter
5. Press harder/softer with the left hand finger to change the tone
6. Choose a different string on which to play the note to change the tone
7. Play two strings at once (you can control which is louder)
(you can do all of these things independently of the other).
Here's what you can do to change the sound of a single note/sound on the concertina:
1. Press harder (louder, but makes the pitch go significantly flat) or softer (quieter, but makes it go significantly sharp).
2. Play more than one note at once (no control over which is louder).
So - yes of course there's a lot that one can do with the concertina, and certainly a lot more than is done by most players (myself included). However, the raw materials (the list above) that it provides are extremely limited. That's the source of its greatest advantages and disadvantages. On the one (negative) hand it can make only a very limited range of sounds, all of which are nearly but not quite "in tune". On the other, if that sound is what you want, it is extremely easy to pick out tunes on, since every note is (almost) in tune, and to make a nice sound on a nice concertina you "just" need to press a button and squeeze.
Apparently a well known concertina player said this, which I agree with: The concertina makes a great second instrument.
Actually - I do disagree with the title of this topic:
... solo violin music is unsuitable for the concertina.
because if the concertina is capable of playing music expressively (and it is), there's no reason why the source of that music shouldn't be violin music.
I would be more inclined to think that the concertina is unsuitable for playing solo violin music, because the violin is just much better at it.