What is the distance from the Arduino to the LED strips.
More important, what is the total length of wire you have to use to the two strips.
Total wire capacitance is your biggest enemy for unterminated lines.
Converting to 12volt won't help.
And driving transistors into saturation makes them slower.
An Arduino output has a low enough impedance to drive low capacitance cable, e.g. CAT-6, to a reasonable length.
Leo..