Both structures are long volatility, but they refuse to be neutral. A strap doubles the call side, so it profits more from an upside break than a downside one; a strip doubles the puts and leans bearish. They are the simplest way to say you expect a big move and think you know which way.
The cost is the point of comparison. A strap costs roughly 50% more than a straddle and needs a correspondingly bigger move to justify itself, so the lean must be genuine. Most traders get the same result more cheaply by buying a straddle and adding a directional vertical-spread.
Example: XYZ at $50 before a binary event. The straddle costs $4.40. A strap — two $50 calls at $2.30 plus one $50 put at $2.10 — costs $6.70 and needs XYZ above $53.35 or below $43.30 to pay.
Related: straddle, strangle, earnings-play, long-volatility-trade