We blew both objectives out of the water. Training time went from 3-6 months to about 2 weeks. We had a variety of modern UI concepts like modals, drop downs and well behaved tables that dramatically simplified the work flow. We also had a full suite of user defined hotkeys, as well as a smart templating system that allowed users to redefine the screen layout on a per use case basis (the screen would be reconfigured based on what customer the user was entering data for example).
For performance, cobol typically requires a server round trip every time the screen changes. We simply cached the data client side and could paginate so quickly that it actually caused a usage problem because users were not mentally registering the page change. The initial screen load took slightly longer compared to the cobol system, but the cobol system required 40 screens for its workflow whereas our system could do everything on a single screen.
I guess my point is that modern systems are capable of much better performance and user ergonomics than cobol systems. We have a lot more flexibility in how UI's are presented that let us design really intuitive workflows. The flexibility also lets us tune our data flow patterns to maximize performance. But most modern development processes do not have this kind of maniacal focus. Systems don't perform because most product owners don't really care that much at the end of the day. Once you care enough, anything's possible.