As you might be aware, the doctrine of God's impassibility has fallen on difficult times, partly because of a misunderstanding of the doctrine, and partly because we crave, more and more, a God that is made after our own image rather than the one presented to us in the Scriptures. With that caveat, I hope I can help answer your question, "who is right" in the (no doubt) friendly discussion between you and your friend.
The first thing we must do when studying a doctrine like God's impassibility is remember that we must never study it (or any other doctrine for that matter) in a way that alienates it from all the other characteristics of God, particularly that of his immutability (the teaching that God cannot change or be changed) because when we talk about impassibility we are speaking about God's inability to change or be changed in regard to his emotions.
The second thing we must do is remember that when we talk about God's impassibility, we are not claiming that God is devoid of what we would describe as feelings/emotions, or that he is some stone-cold, stoic deity. Rather we must understand God, not as expressing emotion/feeling at one moment and not another, but expressing such constantly and without change. God is constant in his love, goodness, wrath, and mercy. God cannot be changed in his anger, love, mercy, or goodness by outside forces, yet he really does love; he really is angry at sin, and really is merciful to sinners. However, he is all these things in fullness and unchangeableness. Therefore, as you say, God is wholly active in these things. He does not run hot and cold in his love for his people, or his anger toward sin. This is what the Confession seems to mean when it states that God is without "passions."
With that said, it is probably incorrect for your friend to claim that God loves as man loves, but just in a more fervent and pure way. Rather he should see God as infinite and never changing (decreasing or increasing) in his love. This, of course, is the God we need! Not one who just loves more than we do, but who love with an infinite never changing love.
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