I say it really depends on your lifestyle. Rent on both places are equally high.

Traffic is heavier in Dubai. Doha's traffic is getting bad as well.

Doha has less places to visit on weekends as compared to Dubai. Petrol is cheaper in Doha. There are more places to visit in Dubai such as malls, shops, bars, etc. Dubai is more cosmopolitan. Doha is still a bit more consevative.

All in all, both places are just 40 mins away by plane so you can always choose...

But if you're out to save... better stick to Doha.