As a former, very frequent flier, I usually found less overhead space in First Class. Most folks in First are there on upgrades because they are frequent fliers. Of that group, more than 2/3 only travel with carry-on's to save time, to prevent baggage issues and to provide flexibilty in case of scheduling/delay issues. Add to that usually at least 2 of the flight attendants have their bags stowed in the First Class overhead bins prior to anyone boarding. Additionally, some First Class overhead space is usually given over to safety (and sometimes in-flight entertainment) equipment.
That is why you will often see First Class passengers lining to be on the plane first. - A lack of overhead space.
I used to fly USAir 737's 50-75 times a year and when I got upgraded, I always asked for row 3 because of the extra overhead space directly behind that row.