I agree - look at long term demand and not short term. What would happen if you graduated today making good money, but then the field dried up and you had to go back to school for another degree (happened to Aerospace Engineers in the late 90's)?
This is a look like for long-term career demand from the Bureau of Labor Statistics: Engineers
Electrical engineers are expected to have employment growth of 6 percent over the projections decade, slower than the average for all occupations.
Compare that to EnvE at 25% per year or CE at 22%. Even ChE (which makes as much or more to start than EE) has a 33% faster growth rate (8%). But, again, you shouldn't use this as your sole decision criterion - look at other factors as well.