The main difference between Minitest and Rspec for ME is the conciseness of the assertion you can impose using Rspec.

minitest_vs_rspec_example

# Minitest
  it "should create a new credit card" do
    from_hash = CreditCard.create_from_hash(hash)
    assert from_hash.valid?
    assert from_hash.number == number
    assert from_hash.cvv == cvv
    assert from_hash.expiry_month == expiry_month
    assert from_hash.expiry_year == expiry_year
  end

# Rspec
context "create a new credit card" do
  subject            { CreditCard.create_from_hash(hash) }
  it                 { should be valid? }
  its(:number)       { should eq number }
  its(:csvv)         { should eq cvv }
  its(:expiry_month) { should eq expiry_month }
  its(:expiry_year)  { should eq expiry_year }
end