I broke the cord on my generator and I want to replace it with something stronger than typical rope. Does anyone have experience with another material?
If you use stronger cord, you'll just break something harder to replace next time. The cord is a "mechanical fuse" - a "weak link" - if it's breaking, it's either quite old, or you are doing something wrong when starting the generator.
Replace it with the same stuff, don't yank it past the point where it turns the generator, and it should last for many years.
Rope and/or cord is available in many different materials, sisal, hemp, nylon, etc. For a generator starter pull cord, you'll want something flexible, strong, abrasion resistant at the very least.
A product on the market used in so many different ways is a cording called Spectra. It's common in fishing lines, as small diameter versions mean low drag, yet fairly high breaking strength.
Spectra is often used as the inner fiber of paraglider suspension lines. Small diameter again, for low aerodynamic drag, but very very strong for keeping the pilot aloft. Another advantage of this material specifically to this application is that the lines have very low stretch and are available in pre-stretched configuration. The tuning of a paraglider wing requires fairly careful attention to distance between attachment points.
In the use of a generator, low stretch means that more (all?) of the force put into the handle will be transferred into the cord and starter spin. You don't want stretchy nylon using up half your energy by stretching out when you yank it.
This material can be considered UV sensitive, but the starter cord typically spends most of its life inside the starter housing.
A quick search on eBay found some spectra line with 50 pound breaking strength for under ten dollars, but it's 0.4 mm in diameter. Not too practical for a pull cord. Even 150 pound stuff is 0.8 mm diameter.
Another term to use in searching is dyneema. A jump over to eBay finds some 5000 pound breaking strength stuff at 1/4" diameter for US$17 for 50 feet. That's a rather good price. The item description also notes in a different manner that it's low stretch. The expression used is that "it doesn't store energy" preventing injuries due to whiplash when broken.
I had a paraglider winch which used 700 pound test spectra/dyneema, equally unsuited for pull cords, as it was 3 mm x 1 mm cross section.
The trickiest part of making a product such as this work in your application will be to ensure you have secure knots at the ends. The stuff is slippery and frequently secured by sleeving and weaving. One end is fed back into the hollow core using a fid, for a substantial overlap. When tension is applied the weave clinches down on the inserted piece and holds stronger than might be believed.
I think it would work well for your application.