when the two matrices are Similar?

Question

Let $a,b,c,d,e,f$ be complex numbers. Determine when the complex matrices, \begin{align*} A= \begin{pmatrix} 2& 1& b& c\\ 0& 2& d& e\\ 0& 0& 2& f\\ 0& 0& 0& 3\\ \end{pmatrix} \qquad B= \begin{pmatrix} 2& 1& 0& 0\\ 0& 2& -1& 0\\ 0& 0& 2& 1\\ 0& 0& 0& 3\\ \end{pmatrix} \end{align*} are similar. Here $A$ and $B$ are said to be similar if there exist an invertible complex matrix $P$ satisfying $P^{-1}AP=B$.
I know that the similar matrices share some same properties. Same determinant, same trace, same eigenvalues, same char. polynomial etc. But in this case, I cannot get a relation between these complex numbers from those properties. So how do we enter the problem?
Idea please.