Civilization – How many beakers does Great Scientist give in Civilization V Gods & Kings

Correct, they are not necessarily the same. You will receive a random technology from those that are available to you, and they will receive a random one for them. This does imply that if you are making use of research agreements, you should try not to "skip" techs that are cheap, since you want the research agreement to give you something as "expensive" as possible.

In general I agree - in late-game, GP are less useful and I usually trade them in immediately for a quick golden age. However, unless you have absolutely everything, great scientists and great engineers do have some value, and there are use-cases where the rest are useful as well, I've listed them below.

Remember golden ages are always great, even if they are short. +gold, +production and no happiness issues.

Great Scientist: if you already have everything then this is indeed useless, but as long as you don't this is still useful. It's true late-game technologies are usually researched quickly but there are a few wonders in late game and being the first to reach them can be nice; furthermore, being the first to unlock Aluminum or Uranium is good because you can plan your land acquisitions better.

Great Engineer: there are some wonders in the late game, and they are pretty good actually. Other than that, great engineers are useful if you create a new city in the late-game; I usually buy a lot of buildings whenever I do this, but a great engineer can save a lot of money by speeding the most expensive buildings.

Additionally, factories are always useful.

Great Merchant: whether you should use the diplomatic mission or the golden age is not always obvious - see my answer to another question to see my opinion. In general I say a diplomatic mission is usually worth more gold, but a golden age also nets production. Custom houses are not worth it, in my opinion.

Great General: I almost always trade them for a golden age immediately, with one exception - I sometimes build citadels in natural chokes or other appropriate locations. From experience, a single citadel in the right spot, backed by 2-4 units, can stop an army.

Great Artist: the most useful type in the late game! Using the culture bombs allows you to reach practically everywhere. I one time used 3 of them to get to just one Aluminum patch in the middle of an icy area (just took a little time because of the cooldown). They can also be used to steal stuff from civilizations and city-states.

Also, landmarks are always nice in cities that already have a lot of +% culture.

Regarding city states: I usually do use great people from city-states, late-game maintenance costs are high but I think a golden age is always worth more than the time it takes them to get to the nearest border, even if it's a golden age lasting just 3 turns.

EDIT as of the June 2011 patch, great person improvements have been buffed:

• Erecting a great person improvement automatically connects a strategic resource if there's one on the tile
• Each great person improvement has an associated technology which increases the tile yield when researched
• Completing the freedom tree doubles the tile yield

This means using great people for improvements is a more viable option now.