Neutrinos and photons Are neutrinos less 'dense' than photons?
I am referring to the fact that neither particle has 'mass' in a conventional sense. In terms of particle interaction, is there a substantial 'size' difference?
 A: The temptation is to think of a particle as a little ball whizzing around space, and it therefore makes sense to ask about the size and density of the ball. The trouble is that this is a fundamental misunderstanding of what a particle is.
Our current best description of particles is using quantum field theory. This describes particles as excitations in quantum fields that pervade all of spacetime. You create a particle by adding energy to the quantum field, and a particle is destroyed by removing energy from the quantum field. Incidentally, this is how particles like the Higgs boson can be created in colliders - the energy of motion of the colliding particles is transferred into excitations of quantum fields where it appears as new particles.
Anyhow, these excitations are delocalised and don't have a well defined position and size, so you can't ask what is a neutrino's size because the answer is that it doesn't have a size in the usual sense. You can try and confine a particle by interacting with it, and this gives you answers like there is a 99% probability that the particle is within this cubic femtometre. But this obviously isn't a size as we usually mean the word. A size would mean a minimum distance below which we can't confine the particle any further.
To confine the particle to smaller and smaller distances needs large and large energies. At the biggest energies we can create (in the LHC) fundamental particles like electrons still have no detectable size. Indeed in quantum field theory there is no minimum size - by making the energy arbitrarily high we can confine particles to arbitrarily small regions of space. String theory may change this if it turns out to be a useful description, but at present no-one knows for for sure if it is.
So the answer to your question is that it has no answer because particles don't have a size, and therefore don't have a density. Sorry!
A: Another take:
Neutrinos are a member of the elementary particle set on which the Standard Model of particle physics is founded. 

Included in the definition of elementary particles is the concept of their being point particles, i.e. no extension in three dimensional space. The Standard Model and its calculational tools have been validated  by the existing data in high energy physics, including neutrino experiments and studies. Thus within our experimental errors the neutrinos also have no extent in three dimensional space, similar to all other particles in the table, including the heavy ones like the Z,W bosons and the Higgs.
Now as John states in his answer string theories give a one dimensional extension to these elementary particles but they are research projects and yet not at the point of giving solid experimental predictions, i.e modifying the Standard Model calculations, at present. I do not know if density would be an attribute that can be applied to strings  in those theories.
