For me, I think there is a very strong and negative cyclical relationship between anxiety and lonelisness.
However, if I were to look at these two feelings completely independent of one another, I would (and actually have), choosen self isolation/lonliness.
When I self isolate, I can get small doses of interaction as needed to not feel so lonely by joining groups/chat on the internet that I relate to or find interesting (eg., gardening, art, graphic design, etc.) or maybe volunteer at a no-kill animal shelter or someplace where I can help others as I can. And in this way, get a little social interaction doing something that feels good to me. Importantly, I would have to do this at a pace I can handle. Things like this can help me with any problems associated with self-isolation/lonliness.
When my anxiety hits - no matter what I do, I cannot stop it and it is beyond extremely disabling for me. Maybe I have social c-PTSD (and no, that is not an offical term in the DSM, I made it up) : )
Happy belated b-day to you!