In my travels, I see a lot of bungee cords lying in the road. I never stop to pick them up. The way I see it, due to the very fact it's lying in the road, it has failed. Whatever someone thought they'd secured with that bungee, wasn't secured anymore. Bungees are quick, easy, and prone to failure.
Tie down straps are a step up. A good tie down strap, when properly ratcheted tight, is fairly secure. I've some good ones and will occasionally use them. The thing I don't like about them is the ratchet mechanism. They are pain to use and more complicated than they need to be.
What I really like is rope. Learn a handful of knots: bowline, clove hitch, square knot, double half hitch and you can fasten down just about anything. I've a few other odd ball knots I use for my own person needs. That's the thing with rope. It's been around for along time. There are special knots for just about any sort of fastening need.
Good rope if fairly cheap these days. Keep a variety of sizes and types handy. Replace old rope when it wears out. Want to really appreciate modern rope? Try making some from natural fibers using primitive methods. It's discouraging to work all afternoon for a short piece of twine.
One winter my lovely wife and I decided to head south to canoe the mangrove swamps of Florida. The snow was deep in NH that year. I put on snowshoes to tamp down a trail to where I kept my canoe and hauled it out. Like an idiot, I didn't store my canoe tying ropes very well. They got wet and froze.
What I should have done is buy new rope. What I actually did was tie down my canoe with half frozen rope. When rope won't bend properly, it makes for some sloppy looking knots. Every time I stopped the car, I checked the condition of the ropes. Surprisingly, everything was fine until about 500 miles south of home, where I hit warmer weather. The ropes became loose and slack all of a sudden. I took about 10 minutes to tighten them up and they stayed tight the next 1000 miles to Florida.