How strange this conversation looks to me !
Having learned Latin first (in secondary school), then mathematics and ancient Greek (at the university) and finally Sanskrit (also at the university, and motivated by my interest in history of mathematics) for my PhD, I find it difficult to imagine things the other way round.
Since I learned the three languages as dead languages, and with the method classical languages were taught in Europe, I was very surprised when I (first journey to India, 1996) met Indian scholars who could speak Sanskrit and even learned it this way. On the other hand, I am myself attracted by learning related modern languages, like modern Greek or Hindi, in order to utter sentences that evoke the ancient languages, so to say. My mother language, French, or Italian, already gave me a sense of the Latin sound.
But, again, for me, Latin, ancient Greek or Sanskrit are languages I imagine only on paper or other supports, on which I learned them and still work (especially Sanskrit that I often translate from manuscripts).
Concerning the differences between ancient Greek and Sanskrit, I must say that I was at first attracted by their mastery in my favourite subject, i.e. mathematics. And in their texts, I found many differences, of course : versification, quasi absence of diagrams, algorithmic approach VS hypothetico-deductive Greek maths, etc. (a long list), on the Sanskrit side. On a more general level, It is true, as you said, that ancient Greek has more intricate rules in syntax. But my feeling is that these rules give me the capacity of translating Greek sentences (with the help of a dictionary and a grammar), while I am too often a quia when I have to give meaning to a Sanskrit compound if I don't have the smallest idea of its purpose. And this is the only domain where I find Sanskrit more difficult than ancient Greek, which means that having learned ancient Greek facilitated the way to Sanskrit (except for the writing (of the nagari) which I considered as a game and mastered rather quickly). I don't know what it would be like to learn these two languages the other way round...