There's no standard criteria for 'high modulus' in the fishing rods so it will vary among manufacturers and product lines, but in general a higher modulus rod will be more delicate.
Higher modulus means that the intended overall stiffness and 'action' characteristics can be achieved with less material, reducing the weight of the rod and increasing its sensitivity. These characteristics make for a better experience fishing with the rod 'in hand', but neither are beneficial in a trolling rod. The downside of less material (and more brittle material) is that it makes the rod less durable, less able to withstand damage. And they cost way more.
Most times when a rod breaks it's either because of prior damage (e.g. bouncing on gunwales, getting stepped on, etc) which reveals itself upon loading, or flexing at too harsh an angle ('high sticking'). Typical fiberglass trolling rods, or something like an Ugly Stik are far more resilient against these abuses than a high modulus graphite rod.