When recruiters ask this question initially, is it good to tell them that I am interviewing at another/competitor firm just so that they may make me a better offer?
or is it better if I say I am not interviewing any where else and this the job I am really interested in.
Depending on your level of seniority there are a number of reasons why you will be asked this. At one end of the spectrum, the recruiter may be looking to ascertain where and with whom, to generate potential leads; at the other end of the spectrum, no recruiter wants to be oblivious to potential competition to an offer, and wants to know if you are interviewing elsewhere so that they can ensure any potential competitor/counteroffer can be dealt with.
Somewhere in the middle is a human being who doesn't take kindly to being lied to when they have proactively approached you for their client, and who would understandably resent having their time and confidence in you wasted.
You wont get a better offer just because you are interviewing with a competitor - companies don't actually think that way, and are usually very reluctant to hire a candidate who wants to instigate a bidding war. This tactic can often backfire - if you don't get the offer from the company in question, and are then seen not to move to one of the others you said were interviewing you, suddenly you look very, very undesirable to the market. And yes, word spreads.
Interview for the roles you are actually interested in. If you are interviewing with several firms, say so, tell the recruiter what stage you are at, but don't mention the company names. Chances are they are all similar organisations anyway.
Treat people like fools and they will soon enough find the only remaining fool in the conversation.