SS - it depends what you want for 'atmosphere':
Luger's is old-school, gruff Brooklyn service. 60 year old surly waiters is part of the charm. It's a historic place, probably the most famous steakhouse in the country. It's also hard to get in, without booking long in advance so it is a bit of a status to go to the original Luger's.
Wolfgang's is more upscale manhattan feel, younger waiters, courteous service. But it's pretty loud.
Steaks are nearly identical, prices about the same as well.
Wolfgang's has a larger menu, more side dishes, and takes credit cards (Luger's does not). I've been to both several times, but usually prefer Wolfgang's. Once you've been to Luger's for the gruff experience that's enough - I prefer a more classy feel. Get the Bacon appetizer at either!!