Comparing any of the Tahoe resorts (I've been to most of them) to Les Trois Vallees ... well there just isn't any comparison in terms of size. I've spent a total of about 9 months (one entire season plus various other trips) in Les Trois Vallees ... have stayed in Meribel, Val Thorens, and Les Menuires. In all that time I still haven't skied everything ... probably 95% of the pistes/groomers ... but only a small % of the off-piste. Although I got good snow at Tahoe, I was disappointed at the lack of vertical.
Note that in Europe there isn't really the same differentiation between off-piste and backcountry ... if it ain't on the marked piste then it's all off-piste. Some of the off-piste is avalanche controlled but little of it is patrolled ... so make sure you have a beeper.
Although the village of Les Menuires is largely as asthetically pleasing as an English politician, it is well worth skiing through Les Menuires to get to the slopes of La Mass. There is some superb off-piste here, plus an itineret
run that is well worth doing if the snow is good ... that's a marked run which isn't maintained ie. it's like off-piste conditions but it is patrolled ... there are a few of these usually marked with a dotted yellow line on the piste map. Some of these are so well trodden though that you wouldn't actually know you were off-piste.
It's also worth taking a trip over to the 4th valley (La Maurien ... excuse my spelling) ... this is over the other side of Val Thorens ... the town of Oriel is at the bottom, but you don't ski down that far. The off-piste there is also superb and it tends to be quieter than elsewhere 'cos most people can't be bothered or don't know what's there. They opened up 2 new chair lifts there about 4 seasons ago ... there was a steep black run at the top which shortly after someone got helicoptered off after breaking their back (I saw them slide about 300 metres over the bumps) they converted it back to off-piste again. I'm not sure if that's still the case.
Over in Courchevel, my favourite runs are around 1600 ... the very long Poma drag lift seems to sort out the men from the boys so it's not too busy.
Basically anywhere away from Courchevel 1850, Meribel Mottaret, or the centre of either Meribel, Val Thorens, or Les Menuires is much less busy. Saturdays are usually the quietest day to ski as it's change-over day for most of the tour companies.
In terms of what the snow will be like in early January ... I can't think of a sensible answer as it could vary from one extreme to the other ... I've had rocks & ice at that time ... and also I have had almost too much snow for them to open the lifts. Here's hoping it's the latter for you. I'll be living it up in Whistler as usual