its the problem solving that kills most people.

this, its not something that you can just learn out of a book like math or something. You gotta always practice, I'm in a CSE major program, I'm in my 3rd year and probably 75% of people from the first year already dropped out to change majors. Thing is in no doubt easy, but depends how much passion and patience you have for it. For me, the logic comes naturally, I find it more difficult to learn the syntax more than anything (I kno its stupid but its just the way I think), for most people its the other way around, they just can't get their heads around the problem. My advice for people going for programming would be, if your interested and your good at logical stuff, then go for it, otherwise stay away from it, your just going to waste your time. Interest in the field alone won't get you far here, you have to have the right set of mind for these things.

It's really about supply and demand. Sure, more and more people are getting involved in computer science, but the demand for software professionals is still MUCH higher than most other fields. There is no question that a CS degrees make it very easy to find a career. I graduated from a top university last year, and had no problem finding a job, whereas even my other non-CS engineering friends were really struggling. We would go to engineering career fairs, and probably 90% of companies there were hiring CS grads, compared to just a handful for other majors.

As for competition within the major, that really depends on the school. Some are very competitive, but if one department is competitive, it will probably be the case that many other departments at the school are as well. It's also worth noting that competitiveness doesn't really have much correlation with overall quality. My department is one of the best in the world, and it had just become the most popular major there, but I felt that I was collaborating with peers more often than competing.

However, with all of that said, this is not the right question to be asking. You should pursue what you are interested in and what you are passionate about regardless of what other people are doing right now. Long-term, you are going to want to be in a field that you enjoy, and that's a lot more important than anything else. Practicality should be a tie-breaker when possible.