Issue with domain bought for PBN

So I recently bought a domain for a PBN, and it is indexed with no spam backlinks. Seemed like a good domain and was working great.

Someone recently put the domain on blogspot, just using blogspots domain and copying the old site that used to be on the domain. Now they rank higher than I do for even the domain name in google. Why? This site has crushed mine for nothing really...

I don't get what you mean. So the blogspot has the exact name as the domain you bought? Well blogspot can be "spammed" with links and have a bit lesser chance of getting penalised. Maybe your competitor have spammed links onto the blogspot site?

Yeah exact same name, just .blogspot. The content on the blogspot is actually the exact same as the old content on this domain. They just copied the old site from this URL and put it back up.

Maybe the owner was using .blogspot in the first place, then bought that domain in question and once it expired, he just reverted back to .blogspot domain? This makes sense.

BlogSpot blogs are actually very easy to rank for as the domain they are on (owned by Google) is highly authoritative.

If you own the copyright on the content you can try and file a DMCA request to get it removed, hell you can even do this if you don't own it and hope that they don't contest it not that I would advise this route at all as it is really a dickish thing to do.

You can file a DMCA at BlogSpot to get them to take the blog down and/or at Google to have it taken from the SERPs. In my experience Google is about as slow as possible to remove SERPs, they are just so freaking slow.