Low-cost leader can certainly be a sustainable competitive advantage. Think GEICO vs. All State.
A lot depends on the service you are looking at, but I think it's important that low-cost be part of your marketing. Advertise the fact that people shouldn't be "paying for features they don't need" or support they don't need. If you are clear up front that you are cheap for these reasons (and are not afraid to fire customers, or at least tell the more difficult ones they should be using the more expensive service), you can sustain that lead.
Be careful, though. You need to think about why your competitor is able to charge more.
An illustrative example is a program called "Final Draft". They make screenwriting software and have been around a long time. Years ago I was curious after hearing the owner discuss how much they sold, how is this company that makes a niche product able to do so much business? How many active screenwriters could there possibly be?
The answer, I realized, is that their business is not made from working screenwriters, it's made from aspiring screenwriters. Every wannabe knows that the pros use Final Draft, so if you wanna pretend to be a pro, you're gonna spend the $100 to get Final Draft so you can feel fancy. This is an awesome advantage for them, and it means I would have a hard time writing a clone and selling it for even $10. The actual software doesn't matter! It's the feelings it gives.
There are tons of products in the Internet Marketing world that have a similar advantage. If your favorite blogger uses it, you feel like a bigshot so you'll pay up for tons of stuff you don't need as s small-timer.
On the other hand, they may just be charging more because they have hired too many people or are being greedy. Up to you to figure this out.