How should I ask for letters of recommendation whose strength is dependent on intended program?
To me, the following progression seems more natural than either of your suggestions:


  I am interested in further studies but I am not sure whether to go to a second masters or a PhD program from here. [Here is my background and here are my career goals.] What are your thoughts?


then


  Do you think you could write a strong letter of recommendation for me for [the kind of program you suggested would be best for me]?


and then, if the answer is yes,


  If I decide to apply to [the other kind of program], do you think you could write as strong a letter of recommendation for me for that program?