HEI providers are sophisticated. They've modeled real estate appreciation across decades and geographies, and they price their products to make money on average across thousands of customers. The 17.5% appreciation share for 10% equity stake (typical Point structure) implies they're betting on moderate-to-strong appreciation — historically true in most US markets.
If they didn't think your home would appreciate substantially, they wouldn't offer the product. The HEI investor wins when appreciation is strong; you win when appreciation is weak or flat. Each side is taking a position on the same uncertainty.
The historical US national average is roughly 4–5%/year long-term, but with massive geographic variation. Coastal California, urban Texas, Florida, Boston, NYC have run 6–10%/year over the past decade. Detroit, Pittsburgh, parts of the Midwest have been much closer to 2–3%/year. Your specific situation matters more than the national average.
If you're confident your area will appreciate strongly (you're in a tech hub, a desirable neighborhood, a high-growth metro) and you can afford the monthly interest — HELOC is almost always cheaper. The appreciation you keep will dwarf the interest cost.
If you're in a flat or declining market, or you're nervous about appreciation, or you can't afford monthly payments — HEI shifts the appreciation risk to the investor. You pay nothing during ownership; you owe a fixed-percentage-of-appreciation at exit, which could be small or zero in a bad market.
The honest answer is that nobody can predict appreciation accurately over 10–20 year windows. The decision should be made on what you can afford monthly first — and only then on what you think appreciation will do. If monthly interest is feasible and you don't want to give up appreciation upside, HELOC. If monthly interest creates real cash-flow stress, HEI deserves serious consideration regardless of what you think the market will do.