You can't tell the differences between the 6000 series and the 7000 series of aluminium bikes by looking at them. But the compounds and qualities of the aluminium are different. They are different to allow for more affordability, to give the buyer a choice between certain aspects of performance versus cost.
When aluminium is cast, it is mixed with other minerals to impart different qualities to the metal. 6061 aluminium is cast with magnesium as its primary additive. 7005 aluminium is cast with zinc as its primary additive. Both formulas have different qualities of lightness, strength and cost. 6061 aluminium is cheaper, thus making a bike built from it more affordable. It's more costly to use zinc as an aluminium additive, making the 7005 series more expensive.
While the strength of most bike frames is not much of an issue, when bike frames continue to get thinner and lighter, strength can be a deciding factor. Magnesium frames are not as hard as zinc frames. This makes the 7005 the better choice if your frame is extremely light such as on some elite road bikes. For mountain bikes that have a bigger tube design, 6061 aluminium is strong enough.
Due to its inherent hardness, 7005 aluminium bikes feel rougher when you ride them. You might not realise it, but bike frames bend when you ride the bike. They absorb bumps and road vibration. The 6061 alloy is softer, making the bike's ride more comfortable. The stiffness of the 7005 frame make its ride more harsh. For smoother riding bikes, choose 6061 frames.
If you care about fashion, keeping up with the latest trends, or want to have the highest priced aluminium bike, you would want to choose the more expensive 7005. 7005 bikes also have more expensive components, and the bike will probably be slightly lighter due to this fact alone. A 6061 bike will cost hundreds of dollars less, though, and will do virtually anything a 7005 bike can do.