I can suggest, and this is vague because I don't know the details at the "left behind" site, that hiring some current UI designers - and I do mean designers - along with some smart front-end developers who are up-to-date with current Javascript frameworks, will let the left-behind company both catch up and provide an excellent user experience on tablets (ok, some tablets are inherently going to provide a poor experience at the moment, but that's not your problem). This also allows you an option to get into the mobile market, if that's applicable.

For many companies with a major web presence, the shift seems to be away from apps to sophisticated HTML 5 websites. They can look very good on just about anything, and will do a lot to provide that "oh, they must be current" kick that seems to be missing. They also allow you to not be beholden to anyone else for distribution or taking a cut of subscription fees, etc. (I love Apple, but all that's built in to their model.)

Another alternative is to build APIs that other platforms can use, whether they're HTML 5 applications or custom apps. In addition, direct access to the APIs by customers is another possible revenue stream - selling enhanced access to the basic APIs, more features, or more capacity for a fee. Don't like our basic interface? You can build the one you want - and we offer support services at $XXX to help.

Essentially, either the service itself has to make is obvious that it's the best, or it needs to provide something else that the competition doesn't: more support, more function, cheaper prices, ... can't make any other suggestions because I don't know the context and I am not a marketer. But the basic is "why are we better, and what should be do to emphasize that? If we're not, what can we do about that?"