Where do they come from?
Natural Stone is mined from the Earth in large blocks and then cut into slabs much like a loaf of bread. Engineered stones are actually man made, but contain 91%-97% natural constituents, mostly Quartz crystals. Engineered stones then have colours, binders, resins and other small ingredients added for colour and consistency.
The price of quartz vary both with the brand and the colour. Granite varies only because of the colour, the largest influence being the country how to calculate square feet of countertop of origin and geographical location. Typically a mid range quartz has a price point that is not far from a mid range granite. There is an upper limit on quartz prices, but granite or similar substances can run into semi-precious rock prices on extreme high end installations.
Is there a difference in strength?
Yes there is. Engineered stone is much stronger than granite, however breakages only normally occur during fabrication or transport and so is a problem for your granite workshop, not you. A good granite workshop will put strengthening bars in the underside of weaker pieces of granite.
Both granite and quartz can vary from batch to batch, though variance is far more likely and generally more pronounced in granite. Granite colours shift throughout a mine becoming darker or lighter both with lateral movement across the mine face and as the mine becomes deeper. The variation of the slabs that have come from the same block is usually undetectable. Quartz hue’s can shift a little between batches, this is much less common with the established brands than it is with cheaper far eastern imports.