The 'Cost' parameter in fitcsvm is usually used to add weights to imbalanced classes, not modifying the constraint on the hyperplane, which is what you're doing in svmtrain.
In the fitcsvm function, the constraint on the hyperplane is called the 'BoxConstraint' and can easily be added the same way as
model = fitcsvm(X, y, 'KernelFunction', 'linear', 'CacheSize', 3000, 'BoxConstraint', C)
However, if you're using the libsvm package, you can still use svmtrain and svmpredict in the newer releases of MATLAB by simply re-making the package in MATLAB. Either method works and I ended up doing the latter.