For me the basket differences can be significant. First, the flow rates can make big differences in how fine you grind, and that can mean a substantial taste difference. Even with baskets that seem like they are in a similar flow category are influenced by their the shapes and holes. I always find this to be true when trying different baskets out on my Londinium. I was switching out the stock basket on the LR with a couple others I had at work, and wasn't getting the results I was having at home. So, I brought in the basket from home and that did it. I purchased the same basket, and now things are good for me. It's all still espresso, but yes, there is a difference.
Will "upgrading" your basket make it better? Maybe, maybe not. Hopefully, some owners of the same machine you have will have some helpful observations.