No, slower. N^300 is polynomial, exp(1e-15*N) is exponential.

Maybe it's easier to understand them if you take log ? log(N^300) = log(N) * 300 and log(exp(1e-15 * N)) = 1e-15 * N

Whatever >0 multiplicative constants a and b you put, a * N will at one point become bigger (so, slower) than b * log(N). In this, that'll happen roughly when N will be somewhat above 10^15, around 10^20 according to a simple guess.