Why are Finder contextual menus different on different macs?
The “Make Alias” option doesn’t appear in the contextual menu if it’s not enabled in the menu bar (the option is in the File menu). You should find that the option is enabled on one Mac, but not on the other. The only explanation I can think of is that this is due to differing permissions or due to differing enablement of the new “System Integrity Protection” feature of El Capitan (if the latter is enabled, it prevents everyone, including the “root” user, from writing in the “System” folder). The “Make Alias” option puts the alias in the same folder as the aliased item, and therefore you need to be able to write in that folder to select the option.

An alternative way to create an alias, in a different folder, is to drag the item while holding down the Option (⌥) and Command (⌘) keys.

There’s an Apple support article titled “OS X El Capitan: Create and use aliases” you may want to check out.