No real differences other than the red face, from what I can find. My understanding (others can correct me if I'm wrong) New Home was the old name for Janome. Then it was Janome New Home. Now it's just Janome. Same great engineering. I was on the verge of buying a used 7700 a few years ago (for $1000) but my dealer said the better idea was her new "reboxed" Janome MC 8200 for $1400. Reboxed machines have maybe been used for a few hours at a quilt show or to demo for a customer before the actual floor model was set up. Everyone I know who has ever had the 6600.7700.8200,8900, and on up the price and feature scale, has loved them.
As for the machine starting to chew heavier fabrics, a couple things could be happening.
1) wrong size needle (thicker fabrics need bigger needle)
2) tension is too tight
3) some machines like to "take a bite" of fabric on the first 2 stitches of ANY fabric, so try using a "leader" piece (thick scrap) and then feed the "real" piece in .
How much does your friend sew? If the machine has had a LOT of use, eventually the motherboard will wear out. The electronic components don't last nearly as long as the motor. So negotiate a fair price accordingly. Or if she is giving it you , GRAB it! Do not pass GO. Do not collect 200. Go directly to Ja(nome). Sorry ,that was dorky.)