The one real difference
Both oils share the same 10W winter rating, so cold-start flow is effectively the same — both pump at the same rate when the engine is cold. The meaningful difference is hot viscosity. 10W-40 keeps a thicker film at full operating temperature, while 10W-30 runs thinner to reduce drag and help fuel economy.
That hot-thickness gap is the whole story here. Some older engines and some warmer-climate recommendations call for a 40-grade, while many others are designed around a 30-grade. The thicker oil is not better in general; it is simply the right choice for the engines whose design and operating conditions call for it.
Which should you use?
Use the grade your owner’s manual specifies for your engine and climate. Because the two share identical cold flow, the choice between them is purely a hot-viscosity decision, and the manufacturer has already made that decision based on the engine’s clearances and operating temperatures.
Some manuals allow both across a temperature chart, permitting 10W-40 above a certain ambient temperature. If yours lists both, follow that chart and stay within the stated conditions. If only one grade is listed, use it, and avoid stepping up to 10W-40 on the belief that a heavier oil protects better. As always, viscosity is separate from specification: whichever grade you run still has to meet the oil standard or approval your manual requires.