The processing is a stabilizer like guar gum added to give more spreadability, stop the cheese from separating (cream from milk) and longer shelf-life. The ingredients on the Finlandia I have sitting in front of me are: Cheese (milk, cream, lactic (I assume whey) proteins, sorbic acid and then some ingredients that must be the stabilizers: INS 330, INS 331i, INS 202.
According to the Interwebs the ingredients in regular Philadelphia are:
Whey Protein Concentrate, Cheese Culture, Salt, Xanthan Gum, and/or Guar Gum). Vitamin A Palmitate.
After reading that, I'd probably go for the Finlandia! They sound pretty much the same thing if you ask me