I am planning to go for a job hunt on a visit visa, which country is best for mechanical engineer jobs and oil / gas jobs? Dubai or Qatar?

I think both of them are good choice to work in. Qatar and Dubai are both rich of resources like gas and oil .So you can find easily a job that fits you. I advise you to do a research before travelling and collect information about the companies that could offer you a good salary and benefits. One easy way to help you is networking; ask your friends or family who live in Qatar or Dubai to give you more in-depth information. 

I think that Qatar is the best considering its highest revenue is from oil and gas sector. On the other hand, we can see that Dubai and Saudi Arabia ae trying to develop other sectors and decreasing the dependence on oil and gas sector which may lead to decrease the demand of jobs in this sector and increasing the demand of other sectors such as tourism, finance, construction and education.

Qatar id good,In dubai recruitments take long time to offer job.

compare salary, perks and living condition then choose what best suited for you.

I guess the United Arab Emirates would be a good place and your second choice will be Qatar if you are not successful with the first one.