I think it depends on if you have experience with building and also the location of the parcel. If you do not have experience, it can be very costly to hire contractors, experts, and project managers.
The pros to building your own house of course are that you can build it exactly the way you want, although many of the remaining vacant parcels left in Los Angeles are relatively steep (on hillsides), and the foundations can often be very costly. I had a client purchase a parcel in Malibu to build a house and the estimated cost of the foundation was about half a million dollars.
If you do purchase a parcel, you will need to do geological, soils, topographical, and other tests to make sure the site is adequate for building. You will also need to make sure there is access to utilities, and that the parcel is able to be permitted by the city for building.
It is possible to get a loan for construction, although not as many lenders are willing to do this.
If you are interested in purchasing a land parcel in Los Angeles, I would be happy to send you a list of available parcels. I can also send you a list of available homes for sale if you would rather purchase a house.
Feel free to contact me directly at (310) 717-1321 or JamieTian@RodeoRE.com.