Whats more important ? A well designed landing page or a well structured Ad ?

They are both important.
An Ad should consist of a solid call-to-action messaging content and the landing page should be clear, easy to use and delivers exactly what the Ad was describing.
Improper landing pages could increase the bouncing rate (The rate of people viewing the page and exiting according to not finding what they are looking for).
But since the landing page measures the success of a user journey, I would look more into the landing pages and focus on conversion rates.
Hope this helps my friend.
Good luck!

both together

well it depends on the target audience and target market segment, if the target audience spend more time on internet then landing page will give best results but if the target audience do not spend much time on internet and they watch tv or news paper then ad will be more useful.
Them medium that a company choose to communicate to its target audience depends upon characteristics of that target market.
The type of contend, appeal used in the ad, the way its presented and all the features of ad or landing page depends on the target audience.

This can be understood and measured if you are familiar or using a marketing framework with a proper funnel, the consumer goes through your marketing funnel step by step, and stops at certain stage, the deeper he goes, the better you campaign is, it should be something like: 1st Stage: Ad impressions.
2nd Stage: Landing Page visits.
3rd Time spent on landing page.
4th ...etc The Ad: Is the eye catching, creative concept presenter and the (Product or Service) value carrier, if well "optimized", then more visits to the landing page will happen, the less clicks on the ad, means that there is something wrong, might be the media you are placing your ad on; which might not have your targeted segment, or the position of the ad is not properly selected, or the ad it self has is not showing the right message.
The landing page: Is the place where the value of your product/service must be as clear, short, straight forward call to action as possible for the consumer, and there you can measure the real impact of your campaign.