An assessment is a process of rating or judging something against a concrete set of standards. For example, if you are assessing a patient you may be taking readings such as blood pressure and respiration rate, and making a judgment on the state of the patient based on the results. An estimation is a reasonable guess or opinion. For example, if someone hands you a box of marbles and asks you how many are in there, without counting them, you would say something like 'In my estimation, the box contains 50 marbles.'

They are almost synonyms ,yet 'estimate ' is more concerned in one of its meanings with values, quantities and numbers. Example : " The current population of India is estimated at so and so .." 'Assess' differs when you refer to assessing a situation for example . So in brief 'assess' is more concerned with the nature and quality of the issue ,while ' estimate ' i associated with the quantitive evaluation , it has more often to do with calculations !

In my opinion, it should be: "I want to estimate the value of my house" "assess" means testing the ability of something or someone. For example, I want to assess the quality of public transport service in Australia.