1)Nightlife:
Miami wins this one. While Los Angeles is home to the entertainment industry, has more variety, it's spread out, and is harder to break into. Miami with her Miami Beach (South Beach) and other entertainment venues, festivals, and 5am call, is just easier to have fun. It's tourist fueled.
2)Amenities:
Los Angeles. It's more than twice as large as Miami.
3)Downtown:
Does "Downtown" mean literally the CBD or the "contiguous urban areas" of each? Either way I'll go with Los Angeles. The CBD of Miami right now is a gentrifying ghetto, Los Angeles has already gentrified quite a bit.
4)Lifestyle:
Don't know what you mean by 'Lifestyle' since there are multiple 'lifestyles' and while Miami and Los Angeles roughly cater to the same glitz and glamour lifestyle, they do it in different ways. I'll remain agnostic.
5)Vibe:
Miami. There is a palpable and noticeable vibe there when you step off the plane that is absent in Los Angeles. No area in Los Angeles matches the energy of South Beach.
6)Cost of living:
I can guess, but let's look at this website:
Cost of Living Comparison Between Los Angeles, CA, United States And Miami, FL, United States
Consumer prices are 5.07% higher in Miami than Los Angeles.
Consumer prices including rent are 4.33% lower in Miami than Los Angeles [meaning rent is more expensive in Los Angeles]
Rent prices are 17.32% lower in Miami than Los Angeles.
Restaurant prices are 0.7% higher in Miami than Los Angeles [virtually identical]
Grocery prices are 3.69% higher in Miami than Los Angeles.
Local Purchasing Power is 0.06% higher in Miami than Los Angeles [virtually identical]
Overall the same lifestyle that will cost you 5,100$ USD in Los Angeles will cost you 4,879.16$.
This does not include two important factors. Miami is in Florida and does not have a state income tax.
If you were a home buyer instead of a renter, real estate prices are way down in Miami compared to Los Angeles [rental rates are not always at parity with actual values in a rental or buyer saturated market]. However HOA fees and insurances will be higher in Florida.
Overall, I give the edge to Miami.
7)Quality of life:
I cannot say. It depends on your interests and your income. I doubt you will secure the same paying job in Miami versus Los Angeles. However, if we could fix your income, for incomes in the range of 150k and down, I'd vote Miami. For incomes higher, I'd be tempted to go with Los Angeles.
8)Neighborhoods:
Los Angeles has more of them.
9)Food:
Los Angeles. LA is a foodie city, Miami is becoming one.
10)Day/Weekend trips:
Miami has Orlando, Keys, and Bahamas, as well as various Latin America destinations. Los Angeles has many national parks, San Francisco, San Diego, and Mexican border cities. Did I mention several mountain ranges?
I guess overall this goes to Los Angeles. If you have to get on your own plane, you can fly many places. Unless you have your own boat in Miami, there is simply not much to drive too.
11)Which is more urban:
Los Angeles is bigger.
12)Big city feel:
Los Angeles feels bigger because it is. By a lot.
13)Beach life:
Miami by leaps and bounds.
14)Economy:
Los Angeles.
15)Weather:
Subjective, I have heard as much praise for Miami's always warm weather as I have heard for LA's always sunny and comfortable. It tends to work out that those in Miami who move to LA complain about how LA is too cool constantly whereas those in LA who move to Miami complain about the summers. In total both have good weather, but Miami's weather is better suited for the beach. However LA doesn't have hurricanes, so I give the edge to LA.
16)Public Transportation:
Both suck, LA has more options for PT but more so for her westside. I guess LA.
17)Traffic:
LA is worse, but Miami is not far behind.
18)Roads/Highways:
Who cares?
Miami wins 5. Los Angeles wins 10. 3 I remained agnostic. 2 of those LA won are really close calls. If you specify your lifestyle and income, it might change the tally in favor of Miami.