I have used both. Best Press has an ingredient that allows it to penetrate the fibers of the fabric faster and so you can press without mess more quickly. I also notice that my iron doesn't get gunky from Best Press like it does from starch. The fabric that I use Best Press on doesn't seem as stiff as when I use starch. It could be that I am using less Best Press however since the cost is so much higher that I'm more careful how much I spray.
When I am starching a larger piece of fabric then I use starch. I use the non aerosol Niagra. I spray the fabric and roll it up and let it rest before I press. If I'm pressing seams and want a little crispness to it or smaller pieces of fabric I use Best Press as I can spray and press right away. I bought a small bottle at a beauty supply store (Sally's) that is meant for hairspray that I use to spray. It gives a much finer mist so my Best Press lasts longer. I buy it in the bottle without the sprayer as it is more economical that way.