How to handle large database updates with node js
Please provide proof that 500k rows is a lot for your database.

Hint In most cases,  it isn't.

Although this answer could befit a Comment, this is a valid Answer.

Databases deal with MILLIONS of rows at a time without a hiccup.  500k is nothing.

Things you need to be aware of when testing the single DML approach 


Undo tablespace (or MySQL's equivalent) 
possibly temp tablespace (for indexes)
locks on a heavily modified table.


If you have proof that one (or more) of those is causing issues, then you should consider Chunking your UPDATE statement.

You haven't given any indication that any of those is a problem.  So, the answer is:  Neither.  Use a single DML.

As far as "process on separate server"...I don't see the need.  I foresee too many headaches with synchronizing the processed rows with any modified data that occured during the Processing.