MATLAB ode solvers for large-scale problems

I am planning to use ode23t to solve ODE systems that have a few hundred states. I have use it already to solve similar, but smaller, problems with a few tens of states, without providing a Jacobian. I am able to get good solutions, and looking at the number of derivative evaluations in the solution stats, I think the process will be substantially quicker if I provided a Jacobian.

I wanted to see if anyone has input on whether there are any inherent performance issues in scaling to a few hundred states and providing a Jacobian. I noticed a statement in Solving ODES with MATLAB by Shampine et al., "The Matlab PSE is not appropriate for the very large systems solved routinely in some areas of general scientific computing ...", and so was wondering if there is anything in particular to be aware of. The book is from 2003, so perhaps some things have changed as well?

Thank you.