At least on iPhone, I much prefer the Spotify interface over the Rdio one. I figured I would give Rdio for a month and I'm already missing the Spotify app. In particular the Search in the Rdio app is abysmal.
Second. I jumped from Rdio to Spotify just for that. I don't understand why people rate Rdio as the best app when basic things like search is broken: search for something, see some bad results, go back to change search, sorry, your search term is gone. Also, the Rdio is app is way too flat and there is big lack of context hint. Often time, I don't know where I am and how to get back to the "parent view", or if there is one.
I despise the Spotify interface. I was a customer for years (UK so it's been available here a while) and switched to Rdio last year mainly because the web and mobile interfaces are so much better (imo).
The Spotify interface has definitely improved somewhat in the last 6 months.
I still use it from time to time and it has got better - but I still think Rdio is miles ahead.