As long as you can write an alert for the condition(s) you need, alerts would be my preferred method. The feedback will be quicker and it will be easier to customize the alert (who gets it, how they get it, etc.) by severity or other criteria. Scanning error logs is better suited for analysis or trending, as you don't want to do it too frequently because of the performance hit.
You can also look at Event Notifications and Extended Events, these have a broader range of events that may be available through alerts. Make sure to do research though, as extended events do not have a native alert mechanism. They would be better suited for a job that polls results periodically similar to a log reader.