So if we are looking for a good sounding speaker system then is it better (sound quality and cost wise) to go for Sub-satellite with active cross over ie line level crossover and then to amplifier for each band and then to respective speakers??
Or these costly full rangers with low powered class A or D amps are the better ??
There's no blanket recommendation for all budgets/requirements that can be made.
1) For the budget-sensitive consumer market, the best bang for the buck is a 2.1 sub-satellite setup. It can give reasonably good sound for almost all sources (PC sound card, CD/DVD player, walkman/discman, cable/satellite TV) at a very low budget.
2) For 2-channel audio, numerous alternatives are available, and it depends on room sizes, type of music, speakers, sources, etc. Active filters driving individual amps and drivers is certainly a possibility, at somewhat higher expense as well as tweaking/tuning for room acoustics.
3) Full-rangers driven by a high-quality 2-channel amp are an important alternative that is now increasingly being chosen by a lot of audiophiles worldwide. The advantage is that colouration and impedance variation from crossover networks is taken out of the picture. This works well with a careful choice of driver and cabinet design, but it is possible to get reasonable results even with budget drivers and sealed enclosures.
A variant of this was recommended by Nelson Pass and others: use a full-range combined with a small helper tweeter driven by a 1st-order 1-way crossover (i.e. just a capacitor in series with the tweeter, or sometimes an impedance pad/matching network). In my experience, this is one of the easiest ways to get a very high-quality audiophile setup at a competitive (but not cheap) budget - the expense will generally be dominated by the driver and cabinet construction cost. It is possible to use an open or semi-open baffle for the full-range.