It depends on the app. The permissions aren't always set consistently by the installers. Check the permissions using "ls -l /Applications" or similar. If a bundle is writable for group "wheel", it's writable for all administrator accounts. There are a number of other system directories besides /Applications as well..
‘wheel’ is used exclusively by root. Unlike Linux and BSD-based systems, Apple uses the ‘admin’ group for sudo. The /Applications directory has group permissions for the admin group, all other system directories are restricted to wheel.
Another question: Is there any real difference between using an admin user and installing all applications into /Applications and using a non-admin user and installing all applications into ~/Applications, if we are dealing with a computer only used by a single person? Phrased differently, if a non-admin user is tricked into running a trojan, that trojan can do to ~/Applications about the same thing as a trojan run by an admin user can do to /Applications.
It depends upon what the application is after. Programs are always run with the permissions of the executing user, unless configured otherwise or additional privileges are needed. This is true for both types of accounts, with the difference that a program executed by an admin may also write where the ‘admin’ group has additional permissions, such as the /Applications directory. However, if an application is after user data or intends to monitor the user, then there is no need to require elevated privileges in many cases.
I think it is still beneficial to operate within the user space as much as possible. It makes you aware of the space in which you are working and shows you what the limits of your permissions are. You almost never have to divulge your user password, because you cannot elevate permissions anyway. With admin accounts, this is not always clear, given that your password gives not only access to elevated privileges but also confidential data in your keychain.
I also think that it is better for software such as Time Machine which operates at a system level and cannot be controlled by a standard user. There seem to be at least some incidents where admin accounts are able to tamper with the Time Machine volume, but I have not been able to confirm this with a standard user.
Moreover, there were vulnerabilities in Apple’s Security framework in the past and sudo itself was not configured with IMO sensible security settings (until Sierra that is).
The bottom line is that running as a standard user bears a negligible hassle and has at least some security benefits. But it is
by no means a panacea.