fMRI data is always acquired as volumes, usually (in humans) with voxels something like 2x2x2 to 4x4x4 mm in size. Some people have argued that for maximum power analyses should concentrate on the grey matter, ideally as surface representations. This strikes me as a bit dicey: fMRI data is acquired at the same resolution all over the brain; it isn't more precise where the brain is more folded (areas with more folding have closer-spaced vertices in the surface representation, so multiple vertices can fall within a single voxel).
But how much of a problem is this? How does the typically-acquired fMRI voxel size compare to the size of the
grey matter? Trying to separate out fMRI signals from the grey matter is a very different proposition if something like ten voxels typically fit within the ribbon vs. just one.
Fischl and Dale (2000, PNAS, "Measuring the thickness of the human cerebral cortex from magnetic resonance images") answers my basic question of how wide the grey matter typically is in adults: 2.5 mm. This figure (Figure 3) shows the histogram of grey matter thickness that they found in one person's cortex; in that person, "More than 99% of the surface is between 1- and 4.5-mm thick."
So, it's more typical that the grey matter is one fMRI voxel wide than multiple. A 4x4x4 mm functional voxel will be wider than nearly all grey matter; most voxels within the grey matter will contain some fractional proportion, not just grey matter. Things are better with 2x2x2 mm acquired voxels, but it will still be the case that a voxel falling completely into the grey matter will be fairly unusual, and even these totally-grey voxels will surrounded on several sides by non-grey matter voxels. To make it concrete, here's a sketch of common fMRI voxel sizes on a perfectly straight grey matter ribbon.
This nearness of all-grey, some-grey, and no-grey voxels is problematic for analysis. An obvious issue is blurring from motion: head motion of a mm or two within a run is almost impossible to avoid, and will totally change the proportion of grey matter within a given voxel. Even if there was no motion at all, the different proportions of grey matter causes problems ("partial volume effects"; see for example): if all the signal came from the grey matter, the furthest-right 2 mm voxels in the image above would be less informative than the adjacent 2 mm voxel which is centered in the grey, just because of the differing proportion grey. Field inhomogeneity effects, scanner drift, slice-time correction, resampling, smoothing, spatial normalization, etc. cause further blurring.
Figure 1 from Fischl and Dale (2000). This folding leads complicates things further: individual voxels still have varying amounts of grey matter, but can also encompass structures far apart if measured along the surface.
This figure is panels C (left) and D (right) from Figure 2 of Kang et al. (2007, Magnetic Resonance Imaging. Improving the resolution of functional brain imaging), and illustrates some of the "complications". The yellow outline at left is the grey-white boundary on an anatomical image (1x1x1 mm), with two functional voxels superimposed, one in red and one in green (the squares mark the voxels' corners; they had 1.88x1.88x5 mm functional voxels). The right pane shows the same two voxels' locations in a surface flat map (dark areas grey matter, light areas white). In their words, "Although the centers of the filled squares in the corners of the red and green functional voxels in (C) are the same distance apart in the 3-D space and points in the same voxel must be within 5.35 mm, functional activations in the red voxel spread to areas over 30 mm apart on the flat map, while activations in the green voxel remain close to each other."
Volume-to-surface mapping algorithms and processing pipelines attempt to minimize these problems, but there's no perfect solution: acquired voxels will necessarily not perfectly fall within the grey matter ribbon. We shouldn't allow the perfect to be the enemy of the good (no fMRI research would ever occur!) and give up on grey matter-localized analyses entirely, but we also shouldn't discount or minimize the additional difficulties and assumptions in surface-based fMRI analysis.