Is doing an M.Sc. in Applied Math a better idea than doing an M.Sc. in Machine Learning considering lack of math skills? Considering that some CS graduates haven't got much in depth knowledge about the mathematical concepts in Machine Learning, which option should be better ?
 A: Well, that would depend where. More information about machine learning is given here What math subjects would you suggest to prepare for data mining and machine learning? But consider the following:
At the University of Waterloo Applicants for the applied mathematics masters program MMath (thesis) normally have an honours bachelors degree in Mathematics. We also welcome applications from students who have completed a degree in Science or Engineering, with a strong concentration in mathematics. Students who have a strong academic record but who have some gaps in their Applied Mathematics background may be admitted subject to the requirement that they complete a selection of fourth year undergraduate courses as part of their graduate program. Minimum grade point average: 78% (in Canada) or equivalent.
At Carnegie Mellon University The curriculum for the Masters in Machine Learning requires five core machine learning courses, and two electives.
These core courses together provide a foundation in machine learning, statistics, probability, and algorithms.
10-701 Introduction to Machine Learning or 10-715 Advanced Introduction to Machine Learning
10-702 Statistical Machine Learning
36-705 Intermediate Statistics

Plus any two of the following courses:
10-708 Probabilistic Graphical Models
10-725 Convex Optimization
15-826 Multimedia Databases and Data Mining
15-750 Algorithms or 15-853 Algorithms in the Real World

MS students are required to complete a Data Analysis Project (DAP). The Data Analysis Project will be concluded by a written report and an oral presentation in the ML Journal Club.
What that means, in effect, is that machine learning is an application of mathematics that is well developed, and that applied mathematics is a general powerful discipline that prepares one for all eventualities, including machine learning :) So, it you will, if your mathematics is not that strong, machine learning will include only a subset of the math you will need for applied mathematics. To put it another way, applied mathematics is taught by people who may throw highly theoretical material at you, i.e., pure mathematics. 
