Doha is VERY different to Dubai - the majority of bars are in the hotels, same goes for the clubs. The good restaurants are also in hotels....the nice beaches are attached to members beaches, or the hotels! Are you seeing a theme here??!?!? Compound living is probably your best option - villa's cost more than apartments, but if you want to be close to a a couple of nice hotels, mall with cinema then West Bay or Al Dafna are probably your best area's to live in. Accomodation costs are high - but a lot of packages here include an accomodation allowance or accomodation provided depending on the company. If you search through this site you'll get a better idea of cost.
If you love Dubai then really think about coming here. Life here is slower and different, if you want a lot of nightlife and the party scene Doha may not be your best option. I like it here and there is stuff to do - just not the same amount of options as Dubai. Lots of people here head to Dubai for the weekend - so consider what is important to you.