In the area of "protection" as DOT and Snell define and test it in their labs. I think it's already been proven countless times that an inexpensive helmet can often be as good if not sometimes better than helmets costing several times more. Keep in mind that I'm talking about lab testing and what Snell and DOT consider measures of safety.
What you get when you get a spendy helmet is (in no particular order):
Graphics choices; lots and lots of cool designs and race replica models
Accessory choices; visors, breath masks, etc
Materials; Carbon fiber and other lightweight materials and construction that don't compromise safety
Features; More vents in often better places, easily removable/washable linings and pads. replaceable and custom fit linings and pads, visor locks, cut outs for helmet speakers, etc
Design; More attention and effort probably went into making the helmet aerodynamic and quiet and solid (particularly if it is a design originally and specifically intended for racing at speed)
And of course you get the personal gratification of wearing the Porsche, Mercedes, or Ferrari of helmets and all the attendant street cred that garners.
Eliminating the potential for protection as a variable assuming that the inexpensive helmets will do at least as good a job in protection. Personally, the two greatest benefits for me of buying a name brand "expensive" helmet is weight and comfort.
Weight, in that in almost all cases, inexpensive helmets for me have proven heavier than expensive ones, and comfort not because cheaper helmets aren't made for human heads, but because it's much easier to go to the Shoei website or the Arai website and get thinner or thicker linings and pads (and a slew of any other goodies) for an absolutely custom fit.
Too many people will buy a helmet that fits their "face" and ignore or not be aware that the most critical measure of helmet fit is the "crown" of your head, where a crown would sit if you were to wear one

If the crown is too small, there is an air gap at the top of your head to where it should contact the inside liner at the top of the helmet interior. This would allow your head to accelerate into the top of the helmet in an impact instead of the crush layer instantly being able to apply all of its benefit at the moment of impact. If the crown is too large, there is a single contact patch at the very top of your head where impact forces would concentrate, and "space" around the crown where your head can move around.
Both are equally bad. The helmet and lining should contact evenly and snugly over the largest contact surface possible around the crown of your head.
To properly fit a helmet, remove the cheek pads and linings and put the helmet on and gauge the crown fit, THEN put the cheekpads back in, if too tight, buy thinner one's and opposite if too loose. Back to the comparison of "expensive" vs "cheap" Your odds that the cheekpads are non removable is much higher in a "cheap" helmet, therefore the odds are greater that the less expensive choice won't have the potential to be properly fitted to your head (this is NOT to say that it's impossible to find an inexpensive helmet that isn't a perfect fit, it just has the odds of being much harder to potentially correct if not)
A helmet is a liability if wearing it is uncomfortable because it becomes a distraction, or a danger if it is too loose and allows your head to knock about inside...