Applying for university 2

If you want the Distinguished Degree, you have to go the University that offers that Distinguished Degree. You should decide which is more important to you, the university your sims attend or the degrees they get.

What if you attend one of the universities and get a normal degree then, later on, you go to the other university to get a distinguish degree?

You can only get a degree once, so you can't get the normal Fine Arts degree and then go back for the distinguished Fine Arts degree. However, you can start at one university and then switch to the other university before you graduate. You might lose some credits but that's probably the closest you'll get to what you want.

For instance, you could start the normal Fine Arts degree at Foxbury Institute for the first 8 credits, then switch to the distinguished Fine Arts degree at the University of Britechester for the last 4. Most of your gameplay would be at Foxbury but you'd still get the Distinguished Degree. You might have to do some extra classes but I don't think it will add more than a week.

The benefits of a distinguished degree only apply when you get a job using that degree. There are no signing bonuses for university, it doesn't have any vacation days, and the only pay you'll get are the scholarships which are the same for both universities.