If you do some research into what is actually required to get certified for DOT, ECE and Snell, you'll find that a DOT sticker alone doesn't necessarily mean a whole lot. One DOT helmet might be much safer than another, because the maker did more than DOT requires. ECE requirements are a little more specific and demanding. Snell has very rigorous requirements for design, construction and testing, and a Snell rating does mean a very high level of protection. When I started riding, I was on a budget and went with a Bilt (Cycle Gear's store brand) that was a good fit and had DOT and ECE. After I learned more, I decided my brain was worth the Snell level of protection and I saved up and got a Snell-rated Shoei. Or I put it on a credit card, I don't remember.
Bottom line, a really cheap helmet is probably not going to protect you very much. A 100 or 200 dollar DOT or ECE helmet will probably do a pretty good job. But the best, verified protection means Snell, and that means several hundred dollars. Is it 3 times safer than a quality DOT or ECE helmet? Nobody can really answer that, I don't think. If it's, just for argument's sake, 50% better and that 50% means you get to ride again tomorrow, how can you put a price on that? You have to make your own decision on what you can afford, and how much a higher level of protection is worth to you. Hopefully this information helps you make that decision.