I wouldn't say that one type has better fidelity than the other. My Sony MDR-7506 headphone is closed back and definitely a higher fidelity device than the Sennheiser HD595.
As far as which to go for, consider these attributes:
-Open back headphones not only let noise into your ears (like your baby crying), they also let your music out. So if you're rocking out in a quiet room, everyone else will be forced to rock out as well. It's not *that* loud, but it is audible.
-The open headphones from Sennheiser are extremely comfy and have a frequency response that, while not the highest fidelity, is quite pleasing to listen to.
-Closed headphones, especially the better ones, isolate you from outside noise and isolate the outside from your music.
Some closed headphones that are semi-circumaural (like my Sonys) can get uncomfortable after a period of time due to the pressure on the ears.
Some other important points to think about:
-Some headphones like the upper end of the Sennheiser line are high-impedance headphones that are not suitable for use with portable music players.
-As far as build quality goes, I have seen no equal to the MDR-7506, MDR-V6, or CD900ST. These are all Sony models.
You will have to weight the benefits of each headphone that you audition. Sennheiser headphones are extremely comfortable, but not the most durable or accurate. The Sony MDR-7506 or V-6 are highly accurate and durable, but not the most comfortable for long periods of time.
Some other headphones I've heard good things about (not heard personally):
Beyerdynamic DT-880
Sennheiser HD-280 (for a lower budget)