Matlab - Fastest way to parallel read many files line by line?
Performing this in parallel using PARFOR should be straightforward if you have the Parallel Computing Toolbox installed. Whether it goes any faster or not depends entirely on the size of your data, the speed of your disks etc. Here's how I would approach it:

function [x, y] = readOnePairOfFiles(name1, name2)
   x = {}; y = {};
   fid1 = fopen(name1); fid2 = fopen(name2);
   %# Read from fid1 and fid2, build up x and y
end

% Use PARFOR to invoke readOnePairOfFiles
x = {}; y = {};
parfor ii = 1:length(dir)
   name1 = fullfile(directory, dir1(ii).name);
   name2 = fullfile(directory, dir2(ii).name);
   [thisX, thisY] = readOnePairOfFiles(name1, name2);
   x = [x, thisX]; %# concatenation reduction to get x and y
   y = [y, thisY];
end