Hello,
It certainly pays to shop around and in my own experience, to move insurer regularly.
In fairness to the AA, they have proven consistently competitive when I've been pricing around over the years and while they have never proven the cheapest for me personally, they are never far out and recently provided my wife with the cheapest quote, for her policy. 123.ie have regularly attempted to push up my premiums without reason (since they were taken over by RSA), so now I'm with Chill.ie who still act as an intermediary, rather than simply an agent of a single insurer, like both 123.ie and insure.ie
While FBD may claim that they are all about "No Nonsense", any time I've asked them for a quote they have produced little more than: garbage, baloney, drivel, gobbledygook, gibberish etc. Infact, any other word I can find when I highlight "nonsense" on Microsoft Word and then select the snyonyms option, applies to my experiences with FBD.