Nowadays, civil Global Navigation Satellite System (GNSS) signals are available in both L1 and L5 bands. A receiver does not need to acquire independently the signals in both bands coming from a same satellite, since their carrier Doppler and code delay are closely related. Therefore, the question of which one to acquire first rises naturally. Although the common thought would tell the L1 band signals which are narrowband, an accurate comparison has never been done, and the decision is not as easy as it seems. Indeed, L5 band signals have several advantages such as stronger power, lower carrier Doppler, or a pilot channel, unlike the Global Positioning System (GPS) L1 C/A signal. The goal of this paper is therefore to compare the acquisition of L1 and L5 bands signals (GPS L1 C/A and L5, Galileo E1 and E5a/b) to determine which one is more complex and by which factor, in terms of processing time and memory, considering hardware receivers and the parallel code search. The results show that overall the L5 band signals are more complex to acquire, but it depends strongly on the conditions. The E5 signal is always more complex to acquire than E1, while the L5 signal can have a complexity close to the L1 C/A in some cases. Moreover, precise assistance providing accurate Doppler could significantly reduce the L5 complexity below the L1 complexity.