Which one is faster? Logistic regression or SVM with linear kernel?
Faster is a bit of a weird question, in part because it is hard to compare apples to apples on this, and it depends on context. LR and SVM are very similar in the linear case. The TLDR for the linear case is that Logistic Regression and SVMs are both very fast and the speed difference shouldn't normally be too large, and both could be faster/slower in certain cases. 
From a mathematical perspective, Logistic regression is strictly convex [its loss is also smoother] where SVMs are only convex, so that helps LR be "faster" from an optimization perspective, but that doesn't always translate to faster in terms of how long you wait.
Part of this is because, computationally, SVMs are simpler. Logistic Regression requires computing the exp function, which is a good bit more expensive than just the max function used in SVMs, but computing these doesn't make the majority of the work in most cases. SVMs also have hard zeros in the dual space, so a common optimization is to perform "shrinkage", where you assume (often correctly) that a data point's contribution to the solution won't change in the near future and stop visiting it / checking its optimality. The hard zero of the SVM loss and the C regularization term in the soft margin form allow for this, where LR has no hard zeros to exploit like that.  
However, when you want something to be fast, you usually don't use an exact solver. In this case, the issues above mostly disappear, and both tend to learn just as quick as the other in this scenario. 
In my own experience, I've found Dual Coordinate Descent based solvers to be the fastest for getting exact solutions to both, with Logistic Regression usually being faster in wall clock time than SVMs, but not always (and never by more than a 2x factor). However, if you try and compare different solver methods for LRs and SVMs you may get very different numbers on which is "faster", and those comparisons won't necessarily be fair. For example, the SMO solver for SVMs can be used in the linear case, but will be orders of magnitude slower because it is not exploiting the fact that you only care are Linear solutions.
I am doing machine learning with python (scikit-learn) using the same data but with different classifiers. When I use 500k of data, LR and SVM (linear kernel) take about the same time, SVM (with polynomial kernel) takes forever. But using 5 million data, it seems LR is faster than SVM (linear) by a lot, I wonder if this is what people normally find?