Advantages of PASMO for tourists:
1) I have gathered from personal experience that SUICA issued by Tokyo Monorail cannot be refunded at a JR station (which means you lose the deposit if you buy one at HND and leave Japan at NRT). By contrast, PASMO can be refunded at HND (Keikyu station ticket windows) and NRT (Keisei railway company ticket windows)
2) O-Sora reported that Pasmo has no fee for refund. I'm not sure if this is correct, but if it is, then it would save users the trouble of zero-ing their balance before getting the refund
Pasmo or Suica for Tokyo / Kyoto visit. Which is better and why?
3) Machines at subway stations allow you to top up cards with coins, (but you can top up SUICA too, so this is an advantage of the machine, not the card)

For residents there may be other advantages to one or the other (e.g. having your commuter pass integrated with your IC card)

Um ... That's all I can think of right now.

A reported advantage of ICOCA is that you can use a credit card to top up at JR West stations ... Sounds very exciting to me.