There may be more people who want to go to New York but there are MANY more law firm positions in New York. Look at the summer associate class sizes in NY compared to DC. Plenty of NY offices have 100+ summers. Not a single DC office has 100, and most have no more than 30 or so.
DC also attracts an inordinate number of top students in my opinion. People who want to go into government, appellate litigation, etc.
So yes, DC is (in my opinion) much tougher. Unless of course you go to school here in which case slightly different story.