Log Shipping or Always on as DR for SQL Failover CLuster
My experience is that an AlwaysOn high availability group, HAG, is easier to maintain than log shipping. Lets set some variables for our scenario.

1.) Your version and edition of SQL Server is SQL Server 2016 Enterprise Edition. We are not on the latest SQL Server patch level. We need to apply a newly released service pack.

2.) The SQL Server database environment exists at a typical small to medium sized company (The active passive AlwaysOn build that you described in your question leads me to this conclusion). This company has a nightly or weekly maintenance window but like most companies the service level agreement is either four or five nines of up time (The database must be available either 99.99% or 99.999% of the time).

Lets look at how each feature allows you, the DBA, to keep the I.T. manager happy by maintaining those up time numbers.

An AlwaysOn HAG gives you the flexibility of being able to fail over back and forth between your AlwaysOn replicas. My assumption is that the primary and secondary replicas are not in close physical proximity to each other. Perhaps they are in different data centers or different racks within a data center. Regardless, If I need to perform maintenance on the primary I can set the availability mode from asynchronous to synchronous, fail over, perform my maintenance, fail back over, and set the availability mode back to asynchronous (https://docs.microsoft.com/en-us/sql/database-engine/availability-groups/windows/availability-modes-always-on-availability-groups). 
  With a properly configured AlwaysOn HAG listener the end user will experience little to no interruption and you'll get to easily maintain that SLA.

Now lets take a look at Log Shipping. Without doing a cut and paste from the Microsoft books online there are five steps that have to be manually performed before you can failover. They can be found here... https://docs.microsoft.com/en-us/sql/database-engine/log-shipping/fail-over-to-a-log-shipping-secondary-sql-server . 

Considering that most incidents and or maintenance windows occur after hours would you rather have an AlwaysOn high availability group that you can easily failover back and forth between replicas or try and get the primary and secondary databases into sync by applying transaction log backups?