365 is nasty, going back 20years useable wise, cloud based crap, hate it, go back to 2010! ( actually I prefer 2003 but hey )
Just for my understanding, when using Office365 does your PC simply download the executables from the Office365 server and then all execution processing occurs on your local PC? That would explain a slightly slower startup time, and then everything should run just as fast once the Office365 programs are resident in local PC memory. Or, do any execution services actually occur on the Office365 server? In this case, performance issues could result from network traffic and server workload.
Office365 is actually office2016. Difference is you pay monthly vs upfront. Break even is about 7 years. Office365 isn't actually bad. I am liking it now mostly because it's a little easier to read the spreadsheets. There are some little shortcuts that are nice. Opening a file from Dropbox is a little annoying because Microsoft is pushing its OneDrive. If you don't need to upgrade, I wouldn't. If you need a new office license, might as well go with 365 or 2016. Fwiw - I run a ton of macros and my spreadsheets are pretty involved.
I took it off clients pcs a few years back, nasty slow web browser server side. Maybe they've upgraded it to proper office with cloud functionality.
I think there are two offices: one you use on the web and one you use on the PC. The PC one is two licenses (pay now or pay monthly). we use web outlook at work and i don't think it's that bad.