You have to keep in mind that MIPs can return the optimal solution, provided enough computation time is given. So if time is not an issue, I would always go for a MIP. Also, MIPs are more flexible in the sense that you can very easily add new constraints, modify the objective function, etc.
On the other hand, with metaheuristics such as local search, there is no guarantee that you will reach optimality, and you might spend a lot of time designing your algorithm which may not work anymore if you need to add a new constraint. That said, they are a great alternative if computation time is an issue. And in practice, computation times are easily an issue if you are working on large data sets.
The choice of the metaheuristic is, I think, a matter of taste (and trend) more than anything. I was told as a student years ago that simulated annealing is no longer considered as an efficient local search technique, and yet it is still used here and there. Perhaps a good way of choosing your algorithm is to find papers where the authors show that their technique worked on the considered type of problem. For example, there are many papers such as this one showing excellent results with Tabu Search for graph coloring.
Regarding trend, there is a famous article called Ants can color graphs from 1997. The article is fascinating, the authors show how you can implement efficient algorithms with artificial ants. But I am pretty sure that if you asked the authors what they think of their article today, they would agree that it was a lot of fun, but they would not use this technique anymore. At the time, using ants was trendy!