Pixels or points for a logo

When you refer to pixel versus point, I assume you are referring to vector point and there are huge differences when it comes to what you want to use when designing a logo. You want to design a logo using vector points and paths - in other words Illustrator because there is no scalability issue. You can then use that original file to prepare any future assets you need. Scale it up for a billboard. Scale it down for a business card. The edges remain nice and crisp. You then export out for the platform you are using - convert to pixels to use on the web. If you are planning to work just on the web, then you should be aligning to the pixel grid. Hope that helps.