Is it better to pass by value for moveable types instead of overloading functions?

I want to reduce copying to a minimum, especially for expensive types/classes. So I could define overloads like this:

void SetParams(const std::map<int, std::string> &params) { mParams = parameters; }
void SetParams(std::map<int, std::string> &&params) { mParams = std::move(params); }
void SetBoardInfo(const DataInfoStruct &board_info) { mBoardInfo = board_info; }
void SetBoardInfo(DataInfoStruct &&board_info) { mBoardInfo = std::move(board_info); }

in a class that has a std::map member variable called mParams and a DataInfoStruct struct member called mBoardInfo.

Since DataInfoStruct has no user defined constructors or destructors I assume that it has an implicit move constructor.

Then I can invoke either one of the overloads with an lvalue or rvalue. However, I could just have one version of each function like so:

void SetParams(std::map<int, std::string> params) { mParams = std::move(params); }
void SetBoardInfo(DataInfoStruct board_info) { mBoardInfo = std::move(board_info); }

In the second way I will always create a copy because I am passing by value, but then I move the parameter into the member variable. If I pass an rvalue I do no copying at all, but for an lvalue there will be one copy made always - which I will do any way if I used the first method.

Which of the two methods is recommended? Are rvalue references best used only for constructors and assignment operators?