There are two related issues that you must deal with: the right to register and use the [word][word][word] domain name and the right to use [word][word][word] as a trademark.
Three mechanisms exist to contest the registration and/or use of a domain name -- through a UDRP proceeding, a lawsuit under the Anticybersquatting Consumer Protection Act, and a trademark infringement and/or dilution lawsuit.
The company that registered (and is presumably using) [word][word][word] as a trademark cannot prevail via the first two mechanisms because it will not be able to establish that you registered the [word][word][word] domain name in "bad faith."
But here's where things get tricky.
The registration of a domain name does NOT, in and of itself, create any trademark rights in the words that comprise the name. Moreover, even if a webpage (or entire website) is published at the domain that is not (typically) enough for any trademark rights to develop in the domain name. The words that comprise the domain name must be used AS A TRADEMARK for trademark rights to develop in the phrase. Explaining how to use a phrase as a domain name AND a trademark is beyond the scope of this response but suffice to say that what must be done, generally, is to brand certain goods or services available to the public with the phrase in such a way that consumers come to associate the phrase solely with the provider of those goods or services.
So ... Let's assume that the registrant of the [word][word][word] trademark is actually using the phrase as a trademark and you merely own the [word][word][word] domain name (but are not publishing a website at the domain or, if you are, you're not using [word][word][word] as a trademark). Under that scenario, the [word][word][word] trademark owner would very likely prevail in a lawsuit that requests the court to order you to transfer your domain name registration to the trademark owner. [Yes, colleagues, even if no likelihood of confusion is shown.]
But ... Let's assume that you do publish a website at the [word][word][word] domain and, moreover, that consumers have come to associate either [word][word][word] or [word][word][word].com with your provision of particular goods or services (the latter of which may, in many instances, include the provision of information about a defined topic). Under that scenario, and assuming that association was created before the other company developed any trademark rights in [word][word][word], YOU would own the trademark rights in [word][word][word] as used to brand whatever it is that you're offering to the public. As a consequence, you cannot be forced to transfer your [word][word][word] domain name and, in fact, may be able to cancel the other company's registration for [word][word][word].
As you can tell, there are way too many variables to provide you with any useful advice. The above is simply general information. Because there is an active dispute over the rights to your domain name you NEED to spend some time with an intellectual property attorney. Good luck.
Your domain name is a website address, which is used to locate your site on the world wide web. You may or may not have been using the domain name as a trademark. The function of a trademark is to designate the source of goods or services, and it may or may not have any internet presence. They're not equivalents.
In this case, it sounds your domain name is virtually identical to your competitor's .net domain name (which you didn't grab) and trademark, so you're competiting in the same TM class for the same consumers, who may very well be confused by the two uses. The difference is that this other company registered their name as a trademark, and you didn't, you've relied solely on your domain name registration. But your domain name is NOT a subsitute for valid trademark rights.
It sounds like your use of the domain name is not cybersquatting and perfectly legitimate, so if this other company institutes a Uniform Domain Name Dispute Resolution Policy proceeding based on infringement of their TM to force you to turn over your domain name, that they would not be successful. But if they instituted a TM suit against you, they have a good chance if winning, since you may have, at best, common law rights depending on how you've used the name on your site and elsewhere, but they have a valid registered TM.
You'll need to see an IP litigator is review your situation, analyze how strong and protectible the mark is, see how you've used your domain name, etc., and give you some specific advice on how to proceed.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.