In Facebook Management, which is more important from your point of view: 1. Number of Page fans OR 2. Quality of Posts ?!

Good question.
Important for whom? If you are a Marketing Manager and want to measure the success of your marketing efforts- increase in no.
of fans is your measure.
No.
of fans helps you compare success of your Facebook page with other Facebook pages as 'apples to apples'.
For more qualitative analysis its important to always keep an eye on the 'quality of your posts' - this is a subjective judgement though.
The quality depends on whether you are adhering to your brand voice and brand guidelines, are you offering news, information that is of value to your followers? etc.

I believe both are co-related . 

You can't neglect importance of any one of them.
Number of fans can't be neglected nor you can compromise on quality of your posts.
The fans are the actually work as the core marketing tool on your page, the more fans you have there will more chances of content going viral.
The cheap and inorganic way of getting fans is useless, these numbers will only showcase on top of your page but important number is of "People Talking About" on your Facebook page.
You can increase fan following by using Facebook owns marketing tools i.e.
Promote posts, create ad, etc.
The more people talking about your posts/page will help in attracting new users.
Once you have successfully understand the cycle of getting real fans, it's time to engage them on regular basis.
Your initial content was designed for your target audience however when you will start getting new likes there will be alot of clutter.
You have to rethink the about content, it's lingo, selection of images and frequency of posts.
People get bored when you keep telling them how good you are.
People appreciate real content that actually is about them rather than you.
Here subliminal marketing method comes in.
Share your message in a light manner that it doesn't sound you are hammering it again and again on their heads.
The better content in the posts more people will like it.
Keep it short and to the point, share real stories rather than always sharing about your services/products i.e.
your company employees pictures, events, birthdays, promotions, celebrations etc.

The quality of posts is always more important. As they show the level of knowledge a person has , his etiquette  and how useful the posts are to the organization and society at large. It is the quality of the fan club that is more important  than quantity.

According to my opinion "The Quality of the posts" because your post generate discussions & increase engagement on the Page to bring more & more Fans.

QUALITY BEATS QUANTITY !

Quantity follows quality, If you have good content people will come as a result - With the right marketing - of course sometimes you need to put your credit card down and advertise but eventually organic reach will become better than paid in terms of exposure, yes your posts might reach more but stories will start to go viral with the least efforts, look at TechChrunch for example.

Social Media is Large, its not just facebook or google+ anymore.
But, when you meant the Fan count or the quality of the posts, doesn't it necessarily mean that it all has to come to the point where what are we trying to project from our social presence.
Quality of content! what do we actually mean from this, does quality means the post that gets most number of likes, shares and talk abouts? or does it mean posting quality content is all about getting the users engaged with our Brand? So when it comes to increasing the bottom lines, whether our social media strategy is contributing will depend on the social media channels we make use of along with the brand engagement created from our campaigns.
Hense Quality along with quantity be able to contribute to the Marketing goals.

your main focus should be on results.

results.

identify your needs and get results.

Its just like asking in business , what is more important...Profits or Reaching Targets.... ,:-) Oblivious it's both..... ..:-)

Both are important, one more point you are missing which is necessary along with both.

**QUALITY OF FANS**

See, getting fake fans is totally worthless as those will not add value in your brand. So, its better to focus on number of quality fans along with the quality posts to involve users for better turnover or brand positioning.