The cause of the feud is simple – Elton was on The Muppet Show and David was not. But David was Jareth the Goblin King – so screw you, rocket man!
On a more serious note …
Personally, I can’t see Elton John being much of a concern to Bowie, although he is a prime example of someone who co-opted the once thrilling and original glam image to help secure his mainstream financial success. I imagine that would irk an artist like Bowie who wrote and performed his own songs for primarily artistic and intellectual reasons.