Yes, time signatures make a real difference. They speak more to phrasing however, than to speed. For a conductor, in this context, phrasing means the number of beats to the bar and the stress placed on each. (Remember that the “denominator” in these signatures gives us a note value and the “numerator” tells us how many notes of that value to the measure.) Given equal metronome values to the quarter note, a bar of 4/4 equals a bar of 2/2 and either will equal two measures of 2/4. Usually, we tend to give some additional stress to the first beat of a bar so, given the same four quarter notes:

• 4/4 suggests one strong beat followed by three weaker beats;
• 2/2 suggests a pattern of strong-weak-intermediate-weak; and
• the two bars of 2/4 will result in strong-weak-strong-weak and sound the most accented.

Before we go further, it is important to note that these are very slight differences in stress, and these principles operate absent any other markings specific to the notes in question. A passage in 2/2, then, will result in a more legato or “flowing” feeling than the same passage with 2/4 in the signature.

You are on to something with your example, but there are other issues that you should know about: fashions and scholarship change. Specifically, Don Giovanni has been re-edited and even re-barred over the years. (I have three different scores, all quite old, where the passage is marked 2/4 so I am guessing that you are looking at a more recent edition.) If you can get to a good music library, you will get a real education by examining more than one edition of the score and listening to old recordings versus newer recordings. You will find, for example, that in the early 1950s, Là ci darem la mano was taken a bit more slowly and in a more accented manner than it is currently.

Consult the summary of subjects for related discussions of establishing a “right” tempo and choosing recordings.