Aside from issues you may run into with your ISP not wanting you to run servers off of a residential connection (check your terms of use), connectivity from the outside world to your home is not going to be nearly as good as if you have a server hosted in a data center.
A typical data center will have multiple high-capacity backbones connecting their building to the internet which not only means better connections between your server and those connecting to it, but greater reliability and redundancy.
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Aside from issues you may run into with your ISP not wanting you to run servers off of a residential connection (check your terms of use), connectivity from the outside world to your home is not going to be nearly as good as if you have a server hosted in a data center.
A typical data center will have multiple high-capacity backbones connecting their building to the internet which not only means better connections between your server and those connecting to it, but greater reliability and redundancy.