How many grafts do I need to cover the vertex(crown)area? Which method is better: FUT or FUE? (Photo)

Photos cannot assess if you would be a candidate for surgery.  Usually this involves seeing a doctor in person.  FUE and FUT are just harvesting methods and is not related to the final results.
Some patients with your hair loss may be happy with 2000 grafts.  Others may not be happy even with 4000 grafts.  It all depends on your goals and realistic expectations.  
Ask your doctor if you can meet with a few patients who had similar hair loss and similar grafts.

Thanks for the question. Based on your photos, the 2000-4000 grafts might be good option for you, but it would be wrong to say something for sure. You should see a board certified surgeon. You can then plan the process together and discuss the results. I wish you all the best. 

To find out what your donor area limits are, your doctor should have measured your donor density and this will tell you how many grafts you have left through your lifetime. Usually, Asians have lower donor densities than Caucasians but that is an average only and you need specific measurements to be done