This was a question posted in quora. I posted my opinion based on my outlook on both of these streams. Whether one is better than the other depends on what is being considered as a common criteria for comparison.
Let's start with scope. A person graduated with a mechanical degree can very well have opportunities to work in the aerospace sector. The aerospace sector is multidisciplinary and people from electrical, coding and other background can easily find work. But the other way is not so. An aerospace engineer is only familiar with the mechanical aspects related to aircrafts. You cannot expect this guy to easily get a job in a heavy machinery industry, for example.
Next grade of comparison is payscale. It is obvious that aerospace is a better paying field compared to field. Here I am talking about the average salary per annum for both the fields. There may be mechanical jobs which pay more than a specific aerospace job. But on an average, aerospace job gets you more bucks.
R and D. Once again this is a tough comparison. Both of the sectors are undergoing numerous innovations over the years. In case of mechanical, there are certain specific fields where R and D is more concentrated than other types of industries. For example, R and D in the automotive fields is much more compared to other types of fields. But for aerospace, every sub-sector is under constant Research and Development.
Job vacancy is a big issue. And mechanical easily exceeds aerospace in terms of available job numbers. This is primarily because mechanical is a broad field. It can be divided into marine, automotive, heavy machinery, thermal, tooling, power plant, and hundreds of sub fields, each of them having numerous opportunities. Aerospace is only aerospace. To be more precise, aerospace is a specialization field of mechanical itself.
So you can see the comparison. Better is a relative term. The grounds of comparison matter a lot. So choose your interest carefully, and don't regret later!