I did not cut this oak beam but I think I can speak for everbody that has used push and pull saws. Yes, you can cut this with a conventional saw but it will take you longer and it will not be as clean a cut. The pull saws have a much thinner blade then push saws and therefore are removing less material ( in width but more in depth) then push saws resulting in less effort for the user.
The harder/denser the wood the harder it is to cut. Try cutting through a knot ( not fun either way) with a push and then with a pull saw. You will notice the difference right away.

My suggestion: Get one of those pull saws and I am sure you will not regret you did.