You're wrong
There's a small overhead associated with calling a synchronized method; that small overhead is exactly the same regardless of how many threads there might be in a program (note that
all Java programs are multithreaded, because even if you only write code in one thread, the JVM supplies many other threads of its own.) For this reason, in any program, the methods of Vector will be a tiny bit slower than those of ArrayList. But only a tiny bit.
A larger difference comes from the different rescaling algorithms they use -- ArrayList grows in smaller increments, and is generally more efficient.