I'm running both 2011 and 2016 on a 2013 iMac and 2014 MBA without issue. Office 2016 will set itself as the default apps and will put the icons in Launchpad instead of 2011. The "Open with" menu will still show Excel or Word v14.x when selected.
Aside from the UI changes, there's little difference between their functions. The biggest difference is the package weight. 2011 used small apps (Word.app is 57Mb) with shared resource files scattered through the \Library folder. The whole suite takes roughly 1.5Gb of storage. With 2016, Microsoft changed to an all-inclusive package system, where each app is packaged with resource files, libraries, fonts, and graphics. Excel alone is 1.76Gb, Word is 1.98Gb, by my count the whole suite is roughly 7.2Gb installed, and the latest v15.19.1 update was 3.6Gb downloaded. This can cause lengthy start times on systems with HDD compared to SDD. On my iMac with 1Tb HDD, Word can take over 40 seconds to launch (MBA with 256Gb SDD takes 10-15 seconds) but once up and running, it's just as fast as 2011. RAM usage is comparable too... Word 2011 with a 2 page resume takes 122Mb and Word 2016 takes 124Mb.
I also believe a Microsoft account is required, even with the single install disc. Any old Hotmail address will do the trick. Office 2016 defaults to opening and saving files to Onedrive but it's just a click or 2 to get to "On My Mac" locations. I've had no issues opening and saving files locally, to Onedrive, or Dropbox. I must admit the main reason I got the Office 365 version is the 1Tb Onedrive storage.
One bug that bugs me... using Ariel font if I Bold it, it displays as Bold AND Italics. Print and PDF export are fine, just the screen display is wrong. Small issue but still... and Ariel is the only font I've found that does it. I have over 3000 fonts installed and there's a short hang while Office sorts them on the drop down list. I believe that Office uses it's own builtin Ariel and not the system font I have installed but the same behavior doesn't show if I use other MS fonts like Calibri.