I have been an amateur recorder player on and off the last 19 years, and in that time, I have tried several different recorders. Of course they have different sounds, which sometimes means they are suitable for different uses.
A regular Baroque-style recorder tends to have a very thin sound for the lower tones - or indeed a very different sound quality, making one sometimes even avoid C and C# altogether, narrowing the useful range of the instrument. Also the pitch tends to fluctuate even with small variation in breath pressure, only very precise blowing making the instrument in tune.
For the Mollenhauer Modern, volume varies more than pitch with varying breath, lending itself to a different kind of expressiveness that I find particularly useful when playing modern music, elegies or slow airs.
A Baroque reproduction recorder as a rule of thumb has more reediness and a sharper edge to the sound, which I often find preferable for Medieval music where the unrefined roughness feels more right to me as well as tending to sound better with other period instruments such as hurdy-gurdy, harp or fiddle.
The Modern on the other hand, has a more rounded, gentle sound, precise yet expressive, and with a bit of softness to it, yet without losing character. I have not tried the grenadilla version, but from what I know of grenadilla vs pearwood, I would expect it to have a louder, even more focussed and centred sound - not my preference, but of course it might be yours. I'd in any case recommend trying before buying if possible.
In my opinion, the Modern sounds better with pianos, guitars and softly-played violins, or playing parts one would traditionally expect played on tin whistles or Irish flutes.
I wouldn't recommend starting playing recorder on just a Mollenhauer Modern as one would get much less training trying to keep the pitch correct, so I believe for students it needs at least to be paired with a baroque-style recorder for balance.
For experienced players, or an intermediate hobbyist like myself, who have played enough to know what they are looking for from a recorder, or someone who has mastered the basics and moved on to putting more personality into their performance, I can heartily recommend the Mollenhauer Modern for its unique playability, dynamic expressiveness and highly accessible extended upper and lower range.
Of course, if you just dabble and don't have any serious aspirations with your recorder-playing - and indeed you feel you can afford it - the Modern will also give you an instrument that will sound more in tune with less effort.