Using like over charindex to search for pattern
The disadvantage is that you need to escape all characters of special significance in the pattern syntax.

Following your previous question it seems the way you do the escaping affects the cardinality estimates.

Testing on SQL Server 2008/2012

SELECT name
/*Copying into a temp table as on 2012 this table is now in the readonly 
 resource database*/
INTO #T
FROM   master..spt_values


Then

SELECT *
FROM   #T
WHERE  name LIKE '%\%%' ESCAPE '\' 


gives an estimated row count of 625.33/627.575. But 

SELECT *
FROM   #T
WHERE  name LIKE '%[%]%' 


gives an estimated row count of 1.8563/1.86296. 

In fact no name values in that table contain a literal % character so the second one appears to be more accurate in this case.

The response to this Connect Item states


  We do not have support for precise cardinality estimation in the
  presence of user defined escape characters. So we probably get a poor
  estimate and a poor plan. We'll consider addressing this issue in a
  future release.