When you click on a word with Chicago, you get fewer possibilities. This seems great because I am often troubled by the large lists of possibilities at Tufts. Am I correct in concluding that Chicago is better?
Not if you need those other possibilities. Depends on who you are and what you need.
Then does Chicago make mistakes in attributing certain meanings to certain occurrences of a word in a text? Have they mistakenly excluded the right answers?
They didn’t individually link each word - otherwise bello in line five of the Aeneid wouldn’t offer both “war” and “handsome”. What’s more, the Chicago version doesn’t offer the verb bellare for bello, showing that its dictionary isn’t as comprehensive.
Again, it depends on your needs.
So, when Chicago doesn’t have extra entries, is it because somebody looked at the text? For example, the last four of six entries here are rarely in play and don’t come up when you use Chicago to check this word in a typical text.
For the vast majority of word forms, no. These various tools use ‘lemmatizers’ — programs to parse each word in their corpus. If you were crazy enough to decide you wanted to run your own personal copy of the Perseus software, you would learn that one of the steps the install takes is for a program to go through every text producing parsing information for each word and slamming it into a database (on old computers this can take days to run). By no means is this always accurate. Even the TLG lemmatizer only gets about 95% of forms correct. I believe some of these tools have lengthy lists of exceptional forms to deal with oddities, but they probably omit a lot, too.
For a while there was a tool in Perseus which allowed people to vote on their choices when alternate forms presented themselves. I forget when that disappeared. I don’t know how accurate people were in their judgements.