After a decade of trying several different knee and elbow pads here’s what I finally settled on:
“Bike” brand volley ball style elbow pads…You don’t want anything that will restrict movement of your arms, you don’t want velcro, and you don’t want hard plastic cups. For your elbows all you want is something that provides a little padding, doesn’t restrict movement, can be worn under a long sleeve shirt / sweat shirt / jacket, and won’t make you wobble when in the prone position (like elbow pads with a hard plastic shell)…
Bike volley ball elbow pads are the way to go. You can find them at Wal-Mart or most sporting good stores for under $20. I use them at work, in classes, and at matches:

Larger version of above photo.

Larger version of above photo.
A contractor in a recent class using the same Bike elbow pads that I have used for several years. You can see that he has good range of movement, the Bike pads prevent any discomfort, and provide a stable platform from the prone position (hard plastic shells make a shooter wobble in the prone position):

Alta knee pads: I have tried several knee pads over the years. I found that Hatch Tactical Knee and Elbow pads were over priced and under engineered. I went through several pair.
Something I found out, along the way about knee pads was that velcro leg straps were a “NO GO”. I found that I could never get the velcro leg straps “just right”, they were either too loose, or more often was the case, too tight and cut off circulation in my legs.
Altas knee pads…They are cheap (around $20), they can be found at your local Home Depot or Lowes, they are very durable, they don’t use velcro…they use a nylon strap that is attached to the knee pad via a buckle attachment…everything you need in a knee pad, nothing you don’t.
The set of Altas that I’m using have been through several classes, SWAT calls, work around the house, etc. and are over 3 years old.
The Hatch knee pads that I used in the late 90’s / early 2000’s were double the price of the Altas, and often times wouldn’t even make it through a 3 day training class before the hard plastic shell would seperate from the soft foam…
From the pictures shown by Failure2Stop, it apprears that Hatch has changed their design and gone to the same attachment method that Altas is using (buckle instead of velcro).
Elbow pads…Maximum range of movement, comfort, and as little restriction as possible. Remember that you are not going to be breaking your fall with your elbows. You just need something between you and the ground in the prone position so you elbows don’t get all scraped up. Just a little padding is all that is needed.
Knee pads. …Maximum range of movement, something that is durable because when you break a fall the first thing that comes in contact with the ground is the knees, something that doesn’t cut off blood flow, hard plastic cup, comfort, doesn’t restrict running, walking, etc.
S/F,
Jeff