Ancient Greek is harder than Latin, and more beautiful.

Latin has a more or less completely regular grammar. There are not too many tenses and moods, and it has a basic working vocabulary that's not too large.

Each Ancient Greek verb has something around 600 different forms, if you count all the conjugations and declinations of the participles. There is a lot more grammar to memorize, and there are tons of exceptions. There are classes of verbs that conjugate based on a separate system, and then very commonly used exceptional verbs that are different from all others. Aside from the active and passive, there's a middle voice. There's about 21 distinct forms of the definite article if you don't count the archaic dual case. There are a whole bunch of dialects with their own quirks. There are also many many more words, most of which sound completely foreign to a modern speaker of say, English or French.

Latin is the language of scientists and soldiers. Learning it involves reading a lot about how many men Caesar sent where to take how many hostages from the insidious Gauls, which he then used as bargaining chips in the treaty negotiations. There's a lot of history to read in Latin. It's elegant, efficient and straight-forward, but it's not as beautiful as Ancient Greek.

Ancient Greek is more lyrical. The pitch accent makes it pleasing to hear. Ezra Pound called Ancient Greek poetry the epitome of melopoeia, his word for melodic poetry. Greek has little nuances and features that slightly alter a sentence, conveying a different shade of meaning, which are impossible to translate. Greek dialogue is fantastic because of this. You actually get the sense of overhearing people talk.

Whereas reading Latin to me feels like walking through the world's greatest historical museum, Greek feels like wandering around in a vast garden full of rare plants and exotic song-birds.

The Latin epic poetry like Virgil is a little bit over the top. It's fantastic, but one has to get used to the overly dramatic Latin emotional sensibility. Greek epic poetry like Homer, is less delicately constructed, but has more raw emotion in it. You get the sense that the poet was actually there and is now telling the story, which happens to be epic.

Anyway, sorry to be long-winded. It's possible to learn both at the same time if you have the motivation. I did that while writing a thesis in a totally different field, and it was a ton of work, but extremely rewarding. I highly recommend it.