Is this problem decidable? (computation of $M_1$ longer than $M_2$ on every input) Is this problem decidable?

Given two representations of Turing machines $R(M_1), R(M_2)$, is the length of the computation of $M_1$ longer than the length of the computation of $M_2$ on every input?

My guess is not decidable. I am not sure, however, how to justify it.

I tried this: Lets enumarate all possible words from $\{0,1\}^*$ and run $M_1$ and $M_2$ simultaenously. If $M_1$ accepts/rejects and $M_2$ is still running, output NO. If $M_2$ stops and $M_1$ is still running, check next word. However, if neither $M_1$, nor $M_2$ do not halt on the word, I am stuck and cannot decide it (because I will get an instance of the halting problem for each combination of word and Turing machine).

Is this reasonable or is it a wrong assumption?
Hint: Let $M_2$ be a machine that on input $n$ runs for $n$ steps roughly, and only consider machines $M_1$ that don't depend on their input. If you could solve your task then you could determine whether a given input-less machine ever halts.