World Cup:
The FIFA World cup has always been the epitome of all football tournaments for fans and players alike. While this tournament started in the year 1930 and is older than the Euros, it is also the only source of income for FIFA. Shifting focus from this tournament would mean reducing the income FIFA makes on the tournament and the funds available for activities for the 4 years in between two World Cups. This could slowly result in the downfall of the World Cup. However, it is seen that since places are reserved for countries from different zones in the World, the smaller and lesser known countries get a chance to play football at the World stage. While this is good for the smaller footballing nations, it often results in one-sided matches when they are faced with strong opposition - not a very interesting sight for fans. However, for the fans it is and always be a month long festival and countries outside Europe also get an opportunity to host it. This means that the economic benefits that come with hosting the tournament for the nation, can be distributed all over the world, instead of concentrating it only in Europe, which is already financially ahead of countries like South Africa and Qatar. FIFA engages in development activities (At its own cost) for football for the nation that hosts the World Cup as it did in South Africa, and these benefits are required more outside Europe to develop football.
Euro:
A handful of teams outside Europe can be called strong footballing nations like - Brazil, Argentina, Chile, Uruguay and a few more. Therefore, the biggest attraction of this tournament is that all the 16 (and next Euro will have 24) teams are strong. This results in tougher matches, played high high intensity even at the group stage making it more interesting for the fans. UEFA makes its income off a lot of sources including the top flight European leagues, the Champions League, Europa League and the likes. The additional viewership and resulting income from adding teams outside Europe, will make less of a positive impact for UEFA than the negative impact it will have for FIFA. Of course, the addition of outside teams gives a chance to players outside Europe to showcase their talent at the tournament. However, to make a rule on how to pick the teams outside Europe will be a challenge and a fair amount of bias to stronger teams will be evident.
Both the tournaments are masters of their own domain and I strongly feel that this sanctity should be maintained. The Euro which originally was called the European Nations Cup, should be ideally featuring European teams only. Each tournament has its set of sparks and means different things to fans from different parts of the world. However, coming from a country that has not participated in either (considering myself a neutral spectator!), I would think that things should be kept to where they are now and the fun of each tournament should be taken in the right spirit.