The biggest difference in Duos is how you approach your long term strategy in the game. There are a few extremely important differences from standard which change the dynamics of the game:

Shard HP:

you have a shared HP pool with your partner, but you fight separately in rounds. This means that if one of you loses but the other wins, the HP impact of the round would be low. If both of you lose, however, you can lose HUGE chunks of your HP. In Standard, it’s not possible to get beaten out of the lobby in the early game. In Duos, it’s absolutely possible if both of you have a terrible strategy/luck. This means that staying competitive with most of the lobby in all stages of the game is very important and both of you going on a losing streak is a terrible, terrible idea. If one of you is strong enough, however, the other one can play more greedily.

Shared Heroes:

you are twice more likely to find upgrades. You can share heroes, which means each one of you is essentially searching for the upgrades of two boards at the same time). This has two major implications: First, buying all relevant upgrades you find is a lot more gold intensive, which means it’s hard to go to 50 gold and a high lvl as fast as in solo. Second, most opponents will be quite a lot stronger compared to solo because of the more frequent upgrades.

Shared XP (and economy):

you share the same level as your partner. This brings an interesting dynamic to the team – you want to run different builds for the sake of upgrades, but at the same time, you want your builds to work optimally at the same level (more on that below).