Suppose we have an arbitrary system of PDEs
$$ \partial_t u - D_1 \Delta u + a(v) u = f(t)$$ $$\partial_t v - D_2 \Delta v + b(u) v = g(t) $$
We want to discretise the system in time. We use the implicit (backward) Euler method. We put $$\partial_t u \approx \dfrac{u(t + \Delta t) - u(t)}{\Delta t} = \dfrac{u^{n+1} - u^n}{\Delta t}$$ $$\partial_t v \approx \dfrac{v(t + \Delta t) - v(t)}{\Delta t} = \dfrac{v^{n+1} - v^n}{\Delta t} $$
My question is: when discretising the first equation, for example, which time step of $v$ and $f$ do you consider, i.e. do we write $$\dfrac{u^{n+1} - u^n}{\Delta t} - D_1 \Delta u^{n+1} + a(v^n) u^{n+1} = f^n $$ or $$\dfrac{u^{n+1} - u^n}{\Delta t} - D_1 \Delta u^{n+1} + a(v^{n+1}) u^{n+1} = f^{n+1}$$
If both are accepted, is one of them more favourable regarding convergence?