Psoriatic arthritis and rheumatoid arthritis leads to bone erosion and joint destruction. Firstly, the term bone erosion must be explained in the right context. Loss of mineralized tissue at juxta-articular sites can be termed as bone erosion. There are only a few chronic disorders which lead to bone erosion. Chronic arthritis is one of them. Such a chronic form of arthritis is psoriatic arthritis. In this, there is destruction of juxta-articular bone. This may also be the case in rheumatoid arthritis.
 
The reason why there is bone erosion involved in case of rheumatoid arthritis is that due to trigger of autoimmunity there is attack on tissues and the membrane which supplies lubrication fluid to the joints for smooth functioning. Due to this attack, there is inflammation of tissues and synovial membrane. Thus there is close proximity between inflamed tissues and the bones. Radiography can be the way of diagnosing bone erosion.  

And another fact which is worth noting is that the most common type of arthritis i.e. osteoarthritis or degenerative arthritis does not cause bone erosion. On the contrary, this situation is correlated with increased bone density and abnormal growths. But, rheumatoid arthritis is directly connected with bone erosion.