Does the confirmation time depend on the fee amount? Or is MultiBit slow due to its thin-client nature?

I tested this with satoshiDICE:

• played 0.5BTC with the Bitcoin-QT client. No fee was charged. Got the reply 14 minutes later.
• played 0.4BTC with the Bitcoin-QT client. Fee was 0.0005. Got the reply within 1 minute.
• played 0.2BTC with the Bitcoin-QT client. Fee was 0.0005. Got the reply within 4 minutes.
• played 0.2BTC with MultiBit. Fee was 0.0001. Several hours have passed, no reply yet.