I like h3 too.) b3 doesn't save us at the queen side in any case, h3 is uncomfortable for black at the king side, we can quickly open the center after black c4 and start active game at the king side.
16. h3 Looks okay to me too and is my 2nd choice after b3. I say its my second choice because I would rather black be forced to recapture on c4 with his pawn instead of his rook. After
16. h3 c4
17. dxc4 Rxc4
Material is still even but his rook is active and he can make threats against our e pawn and our knight that is pinned to our queen on c3. We may have the chance to defend by playing Ne5 (which defends e4 again) and trading off some pieces.