The rough rule of thumb is, yes the wider the range the better.
HOWEVER, it will be harder for the driver to respond to all that frequency, especially single driver(speaker) designs. Therefore, although a certain headphone might be able to respond to a very wide frequency(measured in Hz or kHz) range, it is a matter of how well they are presented that will determine how good the sound is. That and along with other factors as well. There are a lot of IEM/headphones out there that are class leading and yet only need to produce 20Hz-22kHz. It's not entirely a matter of how much it can do, but more of how well it can actually do it. Cheap headphones can do that as well, but some can have muddy bass, peaky highs, too fat mids, thin mids, etc. etc.

Try the Sony XB headphone series, the ones with very fat cushions. Like the MDR-XB300 or MDR-XB500...those have an insane amount of bass.

Oh, I thought you were purely looking for bass.
In that case, the others you mention may have a better sound quality.....in fact seeing your list yeah they are definitely better. I don't know bass wise how much 'quantity' they're able to give, but I'm sure they will be good in 'quality' for the price.

I have not tried any of them honestly. Although did try one of the XB. The 'monster truck tyre' cushions really are comfy and I do wear glasses...although they do look ridiculous. 
I pretended I was interested in the XB so that they'll take it out of the box....I tried it, and said, "yeah they sound alright, but I thought they were going to be less ugly on me". So they put it back in and I walked out of the store.    That's the only way I can audition one where I am.