The way AA is calculated in Rhino 6 has changed some and results vary between GPUs and depending on the resolution of the monitor. I see your GPU is an Intel HD 4400 and the driver for it on your system is a few years old. My first thought would be to look for an updated driver for this card but I don’t want to potentially hurt your performance on Rhino 5. So if you can make sure you have that same current driver that you could reinstall if needed, I’d see about updating it as test for Rhino 6. My guess is that will help the viewport speed.
This link provides some driver options for this GPU.
Other ideas are to try disabling GPU tessellation in Rhino 6, this actually speeds the display on high end GPUs but perhaps isn’t working well with your card and driver.
Driver stuff and updates are handled automatically in my system (I have them on). The driver is actually up to date; the 2015 (15.40) is the latest for this chipset. (while the 2018 download adds Braswell support which is not relevant). Also, I’ve been around long enough not to touch that stuff.
In this case all environmental software factors are the same and Rhino5 is doing something better. This PC is capable of fast viewports and smooth antialiasing and one version of your own software manages to it and the other doesn’t.
I get it. Once a developer gets in a “blame their system” mode it is a dead-end for that customer. Moving on. Case closed.
AA will probably look better for this rig in SR8 which is in release candidate mode right now.
Updating the driver is always the best thing to try first. I get it that this sounds like a cop out and there is a chance that this will make no difference at all. We rewrote the Rhino display engine to be based off of modern OpenGL and have found that small changes have been made to drivers over the years that have helped in both their stability and performance. I would venture to guess that a driver that is three years newer has more content/changes in it than just support for a different chipset.
I have been making changes to Rhino to attempt to work better with these older drivers, but we’re obviously not there yet for your specific set up. This is why I’m suggesting a driver update.