My daughter 's mother wants my daughter to be titer tested for immunity to diseases. How effective is this compared to vaccines?

Poor. Titers are fine, but obtaining the test in order to beaccurate requires frequent testing to be sure the levels remain adeqate. Vaccine research has such standards. Would you really want to do this bloodwork at least yearly?
Yes, but expensive. There's a lot of misplaced fear about vaccines these days. The autism smear has certainly hurt the public health efforts. Your grandparents' generation, with polio rampant, and smallpox a killer, would have given their eye teeth for our vaccines. That being said, titers are an acceptable measure of community; however, re-vaccination has little downside risk and can boost immunity over long term.
It is not effective. Titre testing does not protect you from diseases, it only tells you if you have built up an immunity to certain diseases tested. It is usually reasonable to titre test before receiving an immunization (where able) especially in high risk patients whom an immunization would pose increased risk over "normal population risks".