Did Mad Eye Moody duel Lord Voldemort 1 on 1 during the first and second wizarding war?

There isn't any information to suggest Voldemort and Moody directly faced off. While Moody's boggart is Lord Voldemort (cited from the wiki page), considering Moody's position as an Auror, this might come from facing off against various Death Eaters.

We really can only speculate what Moody did during the Wizarding Wars. Although, you can write a pretty good fanfiction out of Moody's past!

It is unlikely they dueled 1 on 1

As for the First Wizarding War we can't be certain as to whether he duelled him or not. Mad-Eye is a very tough Auror, and he was the best Auror in his prime. However, during Voldy's first rise to power, it must be noted that Voldermort was also largely in his prime as well. Moody was skilled but nowhere near the likes of Dumbledore and Voldemort (who dueled 1 on 1).

In the Second Wizarding War, Moody faced Voldemort at least once and that was during the Battle of Seven Potters (Book 7):

Voldemort sought Harry Potter. Since there were seven Potters, Voldemort didn't get the right one. Naturally he assumed that the real Potter must be with the best Auror (which was Mad-Eye Moody). In reality the Potter who flew with Mad-Eye was in fact Mundungus. When Voldemort appeared next to them, Mundungus 'panicked' and disapparated. At this point, Voldemort had fired a Killing Curse at Mundungus (who was Polyjuiced into Potter). As Mundungus had disapparated, the curse hit Mad-Eye Moody, who was killed.

Unfortunately we are not given any other details of this encounter. Moody and Voldemort certainly met each other, but I doubt there was time for a duel of any sort as Moody was almost immediately killed. So we can be certain there was no 1 on 1 duel at this occasion.

It's unlikely that they dueled. Voldemort largely operates in secret and if he dueled he usually ended up killing his opponent (with the notable exception of Dumbledore vs Voldemort).

Even if Mad-Eye Moody dueled Voldy, Moody's chance of survival is pretty slim. A 1 on 1 duel between them sounds unlikely. It must be noted that he feared the Aurors (note the plurality). Despite this he probably didn't fear an encounter with a single Auror (proved when he killed Mad-Eye).

So, it's unlikely they dueled 1 on 1, though we can speculate that they probably met each other more than once.