The winning answer is....Dana K (edited and Sue W.).! When you have a comparison in the sentence, the subject/object rules are a bit trickier. The sentence can leave out words that complete the comparison, use the subjective case, and still be correct.
The first sentence above is just odd - I don't know what "they" or "them" is referring to but have to guess that some other plants were referenced in a prior sentence. In this case, it would be "they" (the "do" that completes the sentence is implied and doesn't have to be written).
The second one is us.
The last one is "I." If you put "me," you are saying that Sophie was better at taking care of the plants than she was at taking care of "Agatha and me." The sentence is really trying to say that Sophie was better at taking care of the plants that "Agatha and I" [were] - it's OK to leave the "were" unwritten.
This might explain it more clearly:
http://www.grammarbook.com/grammar/pronoun.asp
Rule 5
To decide whether to use the subject or object pronoun after the words than or as, mentally complete the sentence.
Examples:
Tranh is as smart as she/her.
If we mentally complete the sentence, we would say, "Tranh is as smart as she is." Therefore, she is the correct answer.
Zoe is taller than I/me.
Mentally completing the sentence, we have, "Zoe is taller than I am."
Daniel would rather talk to her than I/me.
We can mentally complete this sentence in two ways: "Daniel would rather talk to her than to me." OR "Daniel would rather talk to her than I would." As you can see, the meaning will change depending on the pronoun you choose.