Probably neither. Do a search for body fat calipers. There should be a few threads around. It's generally considered to be the most reliable of the cheap methods.
Any of the hand held systems that measure body fat are relatively inaccurate. Even the larger floor models have only really improved in the last several years. Most of them are based on electrical impedance and have to be recalibrated from time to time. The smaller hand held ones can't do that. They are too basic. Electrical impedance measures the time it takes for the machines to send an electrical impulse through you body. Different materials will transmit that signal faster or slower depending on what it is... eg. fat, bone, muscle mass. The better professional floor model ones can get pretty close to measuring your body fat percentage, percentage of overall skeletal muscle mass and your visceral fat. They also do a comparison of upper and lower body lean muscle mass. But... much of it comes down to interpreting the results properly and having the machine set up properly. Not only are there different algorhythms for gender but also for ethnic background. It's not as cut and dry as people would have you believe. Many things can throw the machine way off... wearing a wrist watch or chain around the neck for example... also the better ones have you complete the circuit for the impedance signal by standing on metallic footpads. Also if you have worked out prior to ingested a lot of food or fluid prior to your test the results can be different as well. Interesting to learn about... but not the be all end all. Usually on top notch gyms will have them. I used to work at one of Asia's premier gyms and we had several. They cost a small fortune... but gyms don't give a crap how you test out because the machine is used as a sales vehicle to sell personal training packages. 99% of the PT's that are running people through them are complete muppets who have no clue what is actually being measured and how. What's worse is they will often measure a Asian female against the algorhythm for an African male - or whatever the machine was actually set to... so the data coming back is full of errors... but it doesn't really matter because they're again... using it to sell PT packages. I've seen PT's promise to get women down to zero % bodyfat. lol.... as if it was even possible. Well maybe if you're dead and mummified... I've seen people hang on the numbers off the print out from the machine as if their entire lifes fitness depended on it. It's only a tool... and one people usually have no clue how to use.
Short of being x-rayed or immersed in a water tank a 7 point caliper test is the most accurate way to go. On a side note why does accurate body fat matter? if you look the same but one system says 10% and the other 16% go with whichever makes you happy and monitor the change. If you're not happy with your fat levels then whatever action you take should be dictated by the old fashioned mirror test and won't change whatever measurement you get.
Scales are pretty accurate for me usually, my room mate is a personal trainer so she also does caliper tests for me. Thing about handhelds and scales is that they are thrown off easily, if you use them use it first thing in the morning before you have had anything to drink or eat.