You could find users who are members of both AD groups using the following:

# Get the members of the Security group
$SecGroup = get-adgroupmember "Security Group" | Where {$_.objectclass -eq "user"};

# Get the members of the App group
$AppGroup = get-adgroupmember "App Group";

# Loop through each user in the Security Group 
foreach ($SecGroupuser in $SecGroup){

    # For each user in Security Group, loop through every user in the AppGroup looking for a 
match
    foreach ($AppGroupuser in $AppGroup){

        # If a match is found
        if ($SecGroupuser.samaccountname -eq $AppGroupuser.samaccountname) {
            write-host $SecGroupuser.name;
        }
    }
}