https://www.iad.gov/iad/programs/iad-initiatives/cnsa-suite....
(Doh... I don't know why I'm getting an invalid certificate authority error when trying to access that site, but Qualys SSL Labs confirms it's a real error. Yikes.)
https://cryptome.org/2016/01/CNSA-Suite-and-Quantum-Computin...
Your web server needs to key and manage many connections/sec, and any delays feed back into my web developers further arguing against the use of TLS. You can generally expect no one will be trying to break your current TLS sessions ten years from now. If that doesn't apply to your situation, you probably have bigger problems, such as the broken CA model.
Both of these scenarios may be different with GPG.
It's probably not secure for a hundred years because of quantum computers. But none of the currently supported algs in openssh protects against quantum computers, therefore there's nothing you can do against it right now.
The arguments for using a longer modulus all reduce down to "you'll have to eventually, why not now?" rather than any new threat against 2048-bit modulus keys.