Your photo on the right shows a cat food can stove. It is unpressurized and is very simple to construct and to operate. Your photo on the left seems like a low pressure stove, although I use a completely different type (like a white box stove that is unsealed on top). It is slightly more complicated to build and to operate. Arguments go on and on as to which is better.
To be frank, I do not see a lot of difference in performance, fuel-wise or time-wise. The burner jet pattern tends to be a lot different. The low pressure burner tends to make a wider pattern (for a wider pot) and the cat food can stove tends to make a narrower pattern (for a narrow mug). However, there are many variations.
Some hikers like something that boils faster. Others like something that simmers longer. I built both, so I take one or the other depending on the cook pot that I am using. In the low pressure type, I made one larger to have more fuel capacity, and I made another one tiny to have less weight. There are a lot of "stovies" around here.