which is most basic

Where would the protonation sites be for the following two compounds be? Which is most basic and why?

I am not sure whether the inductive or mesomeric effect wins out here...would it even be the N that is protonated? could a C be protonated?
I will attach image below...

here are the compounds!

It will definitely be the N that is protonated, of that there is no question.

The pKa difference of the conjugate acids will be small. Nor, really, are alkyl groups electron releasing, as such.
The N, being more electronegative than C or H, will have more electron density on it in the ^tBu species, for the simply reason that there are more electrons to draw to it. Hence, the second is most basic.

Thank you so much! Of course it is the N that is protonated as that is where the lp is localised I don't know why I even suggested protonation C! I agree with your reasoning completely, the inductive effect will push electron density on to the N atom!