My background is related to structural system analysis, so my answer will take into account the input usually used during structural testing.
The effects of sine-sweep excitation on the system response have been analyzed, among the others, in the paper listed below:
G. Gloth, M. Sinapius, Detection of Non-Linearities in Swept-Sine
Measurements, XXI International Modal Analysis Conference - IMAC,
Orlando, Florida, 2003 (here it talks also about non-linearities identification, which is not your case, but still it can give you useful infos about the effect of this type of excitation)
J.A. Lollock, The effect of swept sinusoidal excitation on the response of
a single degree of freedom oscillator, 43rd AIAA Structures, Structural
Dynamics and Materials Conference, Denver, Colorado, 2002
P. Nali, A. Bettacchioli, Beating phenomena in spacecraft sine tests and an
attempt to include the sine sweep rate effect in the test-prediction
Impulse excitation is usually give by means of an impact and this makes it a simple and fast way for measuring frequency response functions. Impact testing produces responses with high crest factors, but it suffers of the same problems as those of random excitation: the input is a broad spectrum and the energy associated with an individual frequency is small.
Both are transient excitations.