Greetings,

There are a few ways to look at this:

- Would you be willing to take your undergraduate subject as optional during UPSC?

If yes, then you can opt for engineering subjects later which have considerably higher chances of success as per data.

- How much time would you spend doing a course?

In an ideal situation, it is always great to get into the civil services at the earliest to have a few years of advantage over others in terms of retirement, seniority and higher posts, etc.

In that respect, Engineering would be good since it is a 4 year course and you do not have to do any internships afterwards, whereas BAMS would take you 5.5. years to finish.

- How much free time would you get?

considering the kind of university or college you join your time would be divided amongst various activities. If you are joining any good Engineering or BAMS university then chances are you won't get much time for your UPSC prep so research on that.

bottom line is - I'd personally recommend you join Engineering as it would be the shortest and will probably offer more free time to prepare for UPSC and you can also choose one of your Engg subjects as optional if you take a liking to them.

do not rush it, decide with ease, best of luck!