The Dake has an arbor that can be shimmed (removal of shims really) to tighten it up again.
The Greenerd, once its worn, its going to be sloppy, because there's no way to tighten up the round column without boring & sleeving a giant part. Have one where I work and its mildly dreadful to use because the end of the ram is dancing around under pressure.
The imports just use a couple of bolt-ends bearing on the ram (maybe bronze slugs if you're lucky) to takeup backlash between the ram and cast housing. It works but its not the greatest design. But then again, how many parts are you planning to press?
I agree that a hydraulic press is a great asset and not the tool for every job. It excels at chassis work on automotive parts and would smash sensitive stuff to the point of ruin. Keyway broaches which get "stuck" need some help to stay alive and not more pressure. The mechanical "feel" is the only way to stop before the critical moment in my opinion.
Ratcheting and then compound leverage are both nice upgrades in your arbor press.