Prada and Burberry have very different histories: Prada is quintessentially Milanese; while Burberry is the epitome of Britishness. Prada’s heritage is in leather goods; Burberry’s is in trench coats. But there are also similarities: both have posted strong growth in the past 10 years, narrowing their scale gap with megabrands like Louis Vuitton and Gucci. But, in the past few months, shares in both brands have lost significant value.We can trace the roots of their recent woes to Asia; China in particular. Not that the Chinese market has been easy for anyone recently. But Prada and Burberry appear to be under greater pressure there than their luxury peers. In its most recent quarter, Burberry saw like-for-like growth sinking into negative territory. Meanwhile, Prada has reported negative growth for the past two years. Any misstep now will only compound the troubles facing these brands.Both Burberry and Prada achieved growth by developing product offerings beyond their core, while retaining very significant centres of gravity. Burberry has expanded from its apparel core into leather and accessories. Prada, by contrast, has concentrated on its leather core, while trying to grow a stronger apparel offering. At the same time, in the past few years, both houses have significantly increased the price of their core offerings. They have also moved toward becoming de facto retailers, withdrawing from wholesale and integrating aggressively downstream.In some areas, though, the two have diverged. Burberry commands a clear edge on the Internet, having reengineered its processes to infuse digital throughout the company. Prada, by contrast, has a history of dragging its feet on e-commerce and even now seems loath to commit fully to what others see as a clear opportunity. Both brands have moved into the beauty segment, but through radically different routes. Burberry recently discontinued its license with Interparfums in order to manage its beauty business directly (though given Burberry’s lack of scale in the segment, I have serious reservations about its decision). Meanwhile, Prada seems to have no intention of dropping its well-established licence with Puig.But at both companies, 'brand religion' may have played a part in their respective woes. Burberry and Prada are among the few major, listed luxury companies whose creative directors also sit at the top table: Christopher Bailey is chief executive and creative director of Burberry, while Miuccia Prada is the creative director and majority shareholder of Prada, as well as the spouse of chief executive Patrizio Bertelli. This may go some way to explaining why the two companies have both made moves that seemingly put brand first, business second. Indeed, it is not unreasonable to question some of the extravagant cost commitments and strategic decisions taken on the back of 'brand worship' at both companies.But what’s more than clear is that both Burberry and Prada have work to do to revive their fortunes.At Burberry, it is one year since Christopher Bailey took on the role of chief executive of the company. He still seems to be growing into it, but I expect him to set a new course soon, dropping the “we have a new chief executive but nothing has changed” mantra. The honeymoon with the market is over and times have changed for the luxury sector. Christopher must step up.Secondly, although the phasing out Burberry's Prorsum, London and Brit lines — which will unify the company's product offering under one label by the end of 2016 — may well make strategic sense and reinforce the brand in the long term, in the short term, the move is fraught with commercial risk. This includes the loss of trading space and sales with large wholesale accounts (as multiple shop-in-shop locations in the same stores are eliminated) as well as an implicit upmarket shift and loss in revenue volume. Indeed, in most cases, I have seen brand consolidation result in a de facto upmarket move and a step away from wholesale, as with Marc Jacobs and Dolce & Gabbana.What’s more, Burberry is struggling with desirability. Senior management has conceded that the company needs to enhance its brand desirability in the critical US market. Meanwhile, in China, the tailwind from Burberry’s significant upgrade of its retail network over the past five years may be fading.Prada, on the other hand, has gone overboard in moving its handbags offer upmarket and narrowing its product assortment. Compelling new products at entry price levels would almost certainly help the company get back on its horse.Prada is not shy of switching directions as external conditions change. To wit, the decision to reinforce the company’s ‘Made in Italy’ credentials was a wise one. The company now needs to take a more forceful approach to digital.Companies in general — particularly luxury companies with controlling shareholders as chief executives — are rarely organised for democratic decision-making. Nor should they be. But Prada takes autocratic leadership too far, which risks handicapping the business.Luca Solca is the head of luxury goods at Exane BNP Paribas.