EDIT: Oh my God, I'm so sorry about the length of this. I didn't realise. The Aeneid's definitely more weighty thematically, as x_muso_x says. The audience were basically reading about where they came from - if Aeneas had failed, they wouldn't exist. It's like people get pretty awed reading about the World Wars today, thinking how differently things could have turned out if the other side had won. Odysseus is taking a personal quest - if he'd got eaten by the Cyclops, for example, it wouldn't impact on anything in the long term. It's entertaining to follow, but he's not changing the world.
The Odyssey contains more fantasy, I suppose. There are monsters in the Aeneid, like the Cyclops appears briefly, Scylla gets a mention, etc., and there are those sea serpents which do Laocoon in during the Trojan War, but there's not as much emphasis on them and they seem to be as much in homage to Homer as anything else - the conflict tends to be more between people, and if I'm remembering correctly, there had been some sort of war around the time Virgil wrote it (am I right? I can't for the life of me remember which war), so it'd be possible to relate to. Even when the Odyssey gets scary, it's less 'real' - the main human-to-human conflict is Odysseus and the Suitors, and that ends with him basically just walking in and massacring them. It's not so much there to be nail-bitingly suspenseful, it's just fun watching them get their comeuppance.
You could use the way they treat women as an illustration of the respective levels of seriousness - Odysseus has fun with them, even when the situation's not ideal (okay, Calypso's got him incarcerated, but they still 'find pleasure in making love' the night before he leaves...and yes, maybe Circe does turn his men into pigs, but he can't be having all that terrible a time - doesn't he end up staying a year?), whereas even when things seem idyllic - Aeneas is a widower, in a safe environment in Carthage, and has Dido absolutely falling at his feet (he's the one in the position of power - look at the deer simile in book 4, he's 'hunting' her), but he's compelled by his destiny to put the fate of the Romans before himself. You could argue that as soon as a hero has to stop being selfish the epic immediately becomes more serious. And the chasm between the two heroes widens when you consider Odysseus has a wife back at home.
Kinda tough to argue in favour of the Aeneid being the
less serious work *thinks*. You could look at the subplots following the sons, I guess (although Ascanius's is hardly a subplot, but even so). Telemachus is making a journey of massive personal growth - he spends the first couple of books moping about and waiting for his father to come back and sort things out for him. He makes a couple of mistakes when he's starting out (I would argue that he gets a bit too disrespectful to his mother at times, for example, and he gets a bit hysterical when he's making his speech in - is it Book 3?) but by the end of the epic he's slaughtering Suitors alongside Odysseus.
Ascanius, on the other hand, could almost be seen as being there for light relief - obviously he's important since he takes charge of Rome when his father dies, but that's outside the narrative. He tends to be presented in situations like the hunt in Book 4 where he's praying for something ridiculous like 'a lion or a foaming boar' to come down from the mountains - we know even an adult would see that as pretty challenging, and he just seems kind of endearing for thinking he'd be able to handle it. There's also the bit in the funeral games where he comes out with some of the other younger Trojans and they put on a horse show, mimicking the adults - it's sweet, and he never really seems to mature fully. It seems like Pallas grows up more rapidly than Ascanius later on - we see him leading an army in Book 10, which I don't THINK we ever observe Ascanius doing (feel free to correct me if I'm wrong). His story isn't the serious bildungsroman that Telemachus's is.
Oh, think about the respective Underworlds, maybe? Aeneas has a tougher time in his, arguably, given that he has to actually go down *into* the Underworld whereas Odysseus can just sit there and lure the ghosts up with his little puddle of blood. Obviously neither of them has a super fun time, but the Odyssey treats it more entertainingly, with the list of people and their stories who the audience would have heard of, whereas Aeneas's is more of a serious journey which gets all sad when he speaks to Achilles who says he'd rather be the lowliest man on earth than king of all the dead. Also there's more emphasis on the world itself and less on the people in it in Virgil's underworld - therefore less interesting/'entertaining', more nightmarish.
Also. There are jokes in the Odyssey, kind of (or at least one joke that I can think of). There's a line in book 1 which is translated as 'Why are you at odds with Odysseus?' (Athene to Zeus) - I don't know the original Greek, but perhaps someone more knowledgeable than me could venture it. It's wordplay, anyway, and I can't think of anything quite like that in the Aeneid.
Wow, this has come down pretty heavily on the side of the Aeneid being more serious, but I suppose it was always going to. I suppose you could argue that the gods in the Aeneid are more petty and therefore less intimidating/serious, but that's a bit tenuous. Anyway, I'm just throwing out ideas, and I suspect a lot of them are rubbish (if I've ignored a massive wodge of evidence in any of this PLEASE tell me, I've got the exam on Monday and if I've been incredibly stupid it'd be nice to know before then - I'm well aware that while there's a lot of stuff here, there's a good chance some of it's inaccurate), but I hope this helps a bit, at least. I'm not going to go back and proof-read this, I'm determined to try and figure out the plot of Book 3 of the Aeneid before the end of the evening, so sorry if any of it doesn't make sense, it's just a brain-dump. Woo.