Sometime in your career you will enter an established market with another company who is the market leader. What to do? A knee jerk reaction is to compete on price alone. Not the best strategy.
The first thing you need to understand is how the other company is operating. If they are a division of a large company, chances are they have moved to cash cow mode. Their focus is on bottom line results and they depend upon market inertia to keep them rolling.
You have two choices here. The first is introducing disruptive technology into part of the market space. Without impacting your margins, release a product which is totally targeted at a discrete customers segment and delivers the goods at an order of magnitude better than the market leader. Using your technology you can either deliver the same feature set at a 1/10 price point, or at the same price point deliver features which are 10 times better (installation, ease of use, etc.)
The beachhead approach can also be used. This works where the product isn't that much different from a technical standpoint. In this case, focus on becoming a thought leader in a specialized segment. Pay attention to relationship management and customer service. Make it easy to tear out the competitor's product and replace it with yours.
And when you pick that specialized segment, ensure it is adjacent to many lucrative segments. Once you are established you can easily move into those segments and you will displace the market leader. This approach requires great tenacity and focus. ADD companies should not attempt this.
Just make sure that when you become the big dog, you pay close attention to how you got there and do not become complacent. Constantly innovate your product and your customer relations.