What controls the 'severity' of ApexPages.addMessages(exception)?

Try catching errors as below :

catch(Exception e)
        {
            String error = e.getMessage();
            ApexPages.addMessage(new ApexPages.Message(ApexPages.Severity.Info,error));
        }

Instead of just doing ApexPages.addMessages(e);

Using this in conjunction with Apexpages.hasMessages()

if(some_condition){
                        ApexPages.addMessage(new ApexPages.Message(ApexPages.Severity.Info,'Info not an error'));
        }
        if(ApexPages.hasMessages(ApexPages.Severity.Info)){
        // do something
        }

To set severity dynamically I would use getTypeName() and create a map/ custom setting with exception key and severity value

http://www.salesforce.com/us/developer/docs/dbcom_apex230/Content/apex_classes_exception_methods.htm

Here are some examples of how to add messages with different severities and how they are outputted:

Confirm/Success:

ApexPages.addMessage(
     new ApexPages.Message(ApexPages.Severity.Confirm,'Sample Success Message'));

---

Warning:

ApexPages.addMessage(
    new ApexPages.Message(ApexPages.Severity.Warning,'Sample Warning Message'));

---

Informational:

ApexPages.addMessage(
    new ApexPages.Message(ApexPages.Severity.Info,'Sample Informational Message'));

---

Error:

ApexPages.addMessage(
    new ApexPages.Message(ApexPages.Severity.Error,'Sample Error Message'));

---

There's a great answer in this question that has lots more detail: Difference between the multiple messaging options in Visualforce?