Floating islands and days lengths

I'd guess that it would like being on Everest. You'd get longer days than the land directly below but I don't think it would be more than a few minutes morning and evening if you are talking about an earth-sized planet. +- 10 miles on a radius of something like 3950 isn't a lot...
The day lengths would still vary depending on the time of year [assuming an axial tilt like there is on Earth].

 

If the island is fixed in place above a spot on the ground then the day would be 24 hours (which actually goes for the top of everest as well). The length of the day is determined by the earth going round once. This means the length of a day is the same for all the places on the earth, since they all complete a round in the same time. Things higher up move faster (because they travel further), but they get to the same spot at the same time.

Now, there's a few things to consider.
- daylight might last longer. After all, if you're higher up, stuff is less likely to be in the way to block sunlight. Also, since you're higher up, you can look over the horizon a bit further then someone on the ground. It's not a huge difference, but it should be noticeable.
- if the island is free-floating and it moves at a decent speed, then how long a day is will depend on the direction it is traveling. Think of traveling in an airplane. If you fly directly east, your day will be shorter, since you're flying against the movement direction of the sun, while if you're flying west, your day will be longer since you're flying with the sun (trying to keep up).

 

I should have been clearing that I meant Day[light] as opposed to Night[-time]...