There are good reasons for both types. Real natural dyes are acutally very deep and bright. From looking at your pictures I thing none of your rugs is made using natural dyes. The red one is chimical chrome dye for sure, the other one is most likely chrome dye and bleached and washed to death as Sharafi & Co. posted before.
Chrome dyes are used in all textile industry and if the dye master is expirienced He can get a result that looks like natural dye. Vegetable dyes are more difficult to use and very expensive compared to chrome dyes.
Some producers of Chobi rugs really use natural dyes, but today more than 90% of the production is low grade commercial and there the dyes are always chrome.