Simply put - Quality has two very different connotations - quality of design and quality of conformance.

Likewise, Innovation has at least three different modes - continuous, dynamic and disruptive.

You could possibly now plot a 3x2 matrix and have a review of your question.

I agree with Mr. Mukul P Gupta sir. Anyways, it's an interesting question that can put every other thinking mind into a puzzle! Congrats

Another dimension that you need to take into account is the type of strategy the company is following. Innovation is more suitable when you follow a diversification strategy rather than when you are following a low cost strategy

 are there some important theories? 

In the pre-industrial age that closed in the early 1800s, many organizations could survive if they just provided "quality" products, with token upgrades to maintain competitiveness. (This method still applies where the lifecycle of market introduction, growth, maturity, and saturation and decline is long; Coca Cola and Pepsi are examples of products that have existed for decades.) But competition now means that most organizations need more than “good products”: they require management innovation that creates "value". Business Model Innovation, available at https://www.researchgate.net/publication/266477090_Business_Model_Innovation; Design Thinking, available at https://www.researchgate.net/publication/266477210_Design_Thinking; Harnessing Creativity and Innovation in the Workplace, available at https://www.researchgate.net/publication/254583219_Harnessing_Creativity_and_Innovation_in_the_Workplace; Innovation in the Public Sector, available at https://www.researchgate.net/publication/266478071_Innovation_in_the_Public_Sector; Sparking Innovations in Management, available at https://www.researchgate.net/publication/254583234_Sparking_Innovations_in_Management; and Sparking Social Innovations, available at https://www.researchgate.net/publication/254583180_Sparking_Social_Innovations, expand on related themes.

Article Business Model Innovation

Article Design Thinking

Article Harnessing Creativity and Innovation in the Workplace

Article Innovation in the Public Sector

Article Sparking Innovations in Management

Article Sparking Social Innovations

thank you to all for your answers. But I think, that quality should be on the first place. But I would like to prove it.

Attached please find our paper on innovation competencies.

Cant think of innovation without quality.

The acid test of Innovation is successful market acceptance of new or improved product, service, process etc

successful market acceptance will never occur where the innovation is of poor quality

If quality is low then there is no innovation

Innovation is more important as it is required to increase the quality of the products and to meet the changing needs of the customers.

In my opinion, the quality is definitely the key factor which enables a corporate house to outperform its competitors and to get the competitive advantage. Any compromise at quality level may disappoint the customers, hence may even affect the performance of a company in an adverse way.

The truth is that they are both important, however without innovation a state of competitive advantage may never be achieved, and disruptive innovation tends to improve on quality as the novel market is created, developed and grown. Deep and repeatable innovation that leads to sustainable competitive advantage is usually created through a good strategic management strategy. 

It depends on the company's strategy. 

Innovation is more important for companies operating in technological markets. Quality is more important for companies operating in commodities.  

Intermediate cases should be analyzed individually.

The relative importance is entirely dependent on the product or service and the strategic approach to the company's perceived market, particularly if you have a number of related products under a Brand Name.  It all depends on how you wish to position one or all of your products.  Establishing a position of quality, at a quality price level, will allow you to potentially gain greater market share by using that platform to innovate offspring of that branded product.

Quest for quality is pervasive and tend to drive innovation. Innovation is the manifestation of qualitative superiority in product, process and technology. Although both quality and innovation are important for creating competitive advantage, I feel quality is the prime factor.

Innovation is superior because it also covers quality.

Quality is important because innovation without quality may not work.

It depends on who you are competing against, and what the market (i.e. the customer) values.  We all make purchasing decisions based on 'Value', and that value is different for different people.  some potential customers value a low price, some are looking for quality, or cool design, or speed of delivery, or 'new' innovative stuff, etc. 

Rolls Royce and Louis Vuitton compete in different areas to Ford and Old Navy !!!

Realistically, we all make 'value judgements' based on a combination of the above factors, and an organization has to find a 'niche' where there are enough potential customers with a 'similar' value mix to generate sales and profit.

The other thing is that these factors change over time with environmental, social, demographic and economic pressures that effect the environment that the organization is competing within.

It is up to the organization to 'decode' all this to ensure that they are competitive...

I hope this helps...

Both Quality and Innovation are important for a product. However, they are applicable as follows: 

1) Quality is considered as competitive factor, when there are similar products already in the market. (Example: Cars, Bikes, etc)

2) Innovation is a competitive or in fact a winning factor or is a required factor, when the product category itself is new in the market. (Example: Apple iPod, iPad, etc)

Quality is considered in one scenario and innovation is considered in other scenario. Both can be considered in some other scenarios.

All the best. 

Quite interesting topic but can you narrow down your question? On what scenario is this issue raised? Example: An electronic company? An educational institution? An advertising company? Or an accounting Firm?

Innovation: The New Face of Quality

In the interdependent and competitive global economy one must find true competitive advantages based on features and capability rather than quality alone. Delivering a solution that is unique to each customer is becoming more important than delivering a standard solution with virtually perfect quality. Instead of managing the cost of goods or services, businesses will need to manage growth by offering innovative solutions to customers.

The quality of innovation becomes a differentiating factor. The quality of innovation implies how well each business is equipped to innovate and offer high-volume custom solutions. Thus the businesses will be moving from quality improvement to innovation improvement.

http://www.qualitydigest.com/magazine/2009/apr/article/innovation-new-face-quality.html#

Customer driven innovation is Quality and value based, as customers always look for quality and value for money.

Innovation inspired by human centered design thinking helps to develop products and services valued by customers. Quality is defined by the value placed on the product or service by the customer. Therefore innovation precedes quality in the case, as what is produced comes from considerations of clients behaviors and needs!

In my views if you want sustainable competitiveness than it will be quality oriented innovation because mere innovation will provide short term benefits whereas quality based innovation will generate long term benefits.

EFQM provides a quality-based model for excellence, innovation and creativity for driving international competitiveness by businesses. Currently adopted and practiced by over 30,000 firms

http://www.efqm.org/sites/default/files/overview_efqm_2013_v1.pdf

Innovations strategically ensure quality, but quality itself provides resources for innovations. It depends on the time run.

Hello Vanda, one has to be innovative even in providing quality products or services. Quality is great but because customer has to continually be satisfied and the business landscape is also continuously changing, it demands therefore that quality has to be innovative. Innovation on its own is meaningless if it is not meeting any real needs. Likewise quality will only remain an imagination if it is not delivering real value. So my take is that innovation and quality must mix together to meet customer demand and should even go a step further to dictate customer taste.