Greetings,

First of all you need a criteria to define 'power' and 'influence'. All these services being naturally prestigious, there is a certain level of difference when it comes to their domain of activity, this difference is what most people define as their 'power' . In simple terms the more influential and far reaching a certain posting is, the more powerful people will consider it to be.

Now let me explain in brief what the so called powers of such officers actually entail:

let me start by ranking them in terms of their social influence (how much are their effecting normal people's lives):

1. IAS
2. IPS
3. IRS
4. IFS
5. IES

1) IAS - why is an IAS officer considered influential? simply put an IAS officer, during the early part of his/her career when they are collectors, have a far reaching domain of responsibility. They oversee almost every department in a  district that generates revenue (hence the name, 'collector). Such control over functioning of so many departments puts an IAS in a position to virtually effect so many lives in their districts and that is why people flock around them to gain their favors. IAS officers in later half of their careers are still really influential because they move over to policy making work in various departments, each bureaucratic policy can majorly impact a department or field.

2) IPS - In early career years, IPS officers have direct impact (literally direct) over the citizenry of a district. They interact with the public, deal with their grievances, they can have the authority to arrest, search and even kill (encounter) under certain circumstances, these powers of the police are really unique and effect a lot of people in their daily lives, police is powerful because the people depend and rely on them for protection, exercise of justice and other things, many times these responsibilities are misused in certain ways, unfortunately and hence gives birth to a misconception that the police can do anything to anybody. Later career, IPS officers move away from the field and work on policy policy, budgets, planning, strategies for better policing of a state or move on to central services just like IAS officers.

3) IRS (different from IRAS) - The reason I put an IRS officer above IFS in the list is because we cannot judge the both on the basis of job profile, UPSC preference list and such. IRS stands above in terms of what you call as 'powers' because as I said, the criteria of power and influence involves direct impact on citizens' lives. In that respect, IRS officers handle one of the most import aspects of our economy, taxation and revenue. That responsibility is in an of itself is unique and gives them a wide array of influential decision making powers.

4) IFS - We generally do not interact directly with IFS officers and so they have a clearly defined domain that indirectly affects us in the long run. Meaning that the foreign policies, diplomatic relations that these officers help form with other nations is where their influence is seen most and a normal person living a normal life has no business in that department so they don't need to go to an IFS officer's door to ask for help.

5) IES - IES officers (engineering services) have their own technical exam for selection and are, essentially, 1st class engineers who are concerned with administration of our industrial sector (PSUs and all) so they have a different career trajectory just like IFS officers do which does not involve other citizens as much.

As for their influence, both IFS and IES officers exercise great influence and position of authority in their respective fields but most people like us don't even know who they are but we know who the collector, Chief secretary or SP or Commissioner of a district are.

There you have it, a simple demarcation of what you call 'powers' of the coveted Civil Servants. They are important positions socially as well as politically speaking but at the end of the day their core responsibility is to serve the nation and its citizens.

Hope it helped get some clarity,

Good day!