I'm thinking that's the reason you want to change right? Because its a .co not a .com and either want a .com or something else and as your current domain name has store in it, making the change to a .store domain might actually make a bit more sense.
But if it's for the reason of ranking, .store's don't have any more authority than a .co does. So in answer to your question which one gives more value, from an SEO perspective none of them do. But from a people perspective, I'd say just the .store one Forget about .web one.
.co's do have their own reputation, the same way that people felt about .info's when they were first released but these days, there are many quality authority sites that are a .info.
I gotta give it up for the .info actually, it was a .info that I paid $5 for and sold for $75k about 7 years ago now when mobile phone recycling was kicking off I totally dominated that niche.
Anyway, I know that's about as relevant to you as a nun in a bar full of hells angels but don't come down on your .co so much.
You have to way up the pros and cons.
Obviously if you change domain names, you have to redirect all your old stuff to the new one, not too much hassle but can get tricky.
Then you have to change loads of other things, give out new links, that kind of thing.
But if you don't have that many backlinks with this domain and wont have to do much of that and you feel better with it then go for it!
