A derby (also called bucks or Gibson) is a style of shoe characterized by shoelace eyelet tabs that are sewn on top of a single-piece vamp. This construction method, also known as "open lacing", contrasts with that of the Oxfords.- Wikipedia
Had to do a lil Wikipedia-ing to update myself with what Derby shoes meant. Moving away from the education lets get to the crux of the discussion here. We got 2 similar shoes, Asos one retails for £50 whilst the Dr Martens retails for £90.
Most people would easily pick the Asos one over the Dr Martens cos of the price but then again that would be uneducated shopping. Before investing in one of these you would have to consider a few factors asides from price which include durablity and amount of wear you are likely to give the shoes.
If you're like me and got loads of shoes, i'd say go for the Asos one on durablity terms but if you like your brands and you're a Dr Marten Loyal and you probably intend to rock your bleached denim derby's till death, then the Dr Martens would suit you as they even get better with wear and age.