The hand held one measures more of your upper body fat and the scale, your lower body fat (unless like me you have something like the Ironman tanita which does both.) I find one is nor more accurate than another. You are probably somewhere inbetween the two readings depending on where you retain your fat.
While some of these methods of measuring body fat *might* be accurate for your body type, there is also a good chance that it is wildly inaccurate. I would recommend trying to find one of these machines if you're interested in an accurate measurement:
Many universities have them and will test you for a fee. My local university has one, and they charge $100 for a pair of tests (baseline and followup). If you're in the US, this link might be of assistance in finding one:
My old Tanita scale is whack.
I'm 5-9, about 150...I can get a reading of 34% BF in the morning, then 30% half an hour later after drinking some coffee.
Last caliper at the gym, 24%.
I hate the Tanita. It's going in the trash ;-)
If you have a well rated impedance scale you should be able to get consistent numbers, but most likely not accurate.
People mention using there scales and then the results changing within a short time span, but they also mention, eating, showering, or activity, which even according to the manufacturer will give you varying results. All activity, time of day, surface conductivity, should be kept consistent between measurements to get consistent readings.
I've had a Tanita scale for a couple yrs and the readings are pretty consistent, but the absolute number is definitely off. Also, most manufacturers recommend taking an average of 3-5 weekly readings with consistent testing procedure to get a good reading that week. Then you can compare this to the following weeks average reading. Another issue is the surface condition of your skin, so a quick rub of your feet with water should give you a more consistent surface. One last note, I've noticed women will have even more trouble in keeping testing circumstances consistent due to all the rapid changes that they can incur in a short time span.
From my experience I've found the most consistent time to keep controlled and in terms of body resistance is in the morning after waking up.