You have to remember that L2S is a Object Relational Mapping system, so its trying to to compare objects, and translate to SQL. In L2S, if you want to compare two strings you have to ToLower() both of them for comparison.
Another thing that was a 'gotcha' for me was that in L2S, string comparison will not evaluate correctly if the comparison value you supply is null. So, in your example, if table.Column is null and stringValue is too, your query will not return the correct results (I am basing this on the assumption that stringValue is a variable defined in your code). In order to compare a string to null in L2S, you have to compare it explicitly to null: table.Column == null.
check out this article