is there any other band that can do something similar to what the x-band does? Any that require a smaller antenna and more electrical power?
1$\begingroup$ For all frequencies from MHz upto GHz as well as THz and EHz, a larger antenna will deliver a stronger signal on reception and a smaller beam width on transmission. $\endgroup$– UweMar 15, 2020 at 14:52
The quick answer: yes, Ka-band. There are other deep-space frequency bands, such as S-band, L-band, and UHF, but Ka-band offers unique advantages — but some disadvantages too.
You can always trade antenna size for electric power. Boost the power without changing the frequency, and you can get the same data rate from a smaller antenna. Increasing frequency allow you to improve the parameters of that trade.
X-band isn't qualitatively different from other frequency bands used for spacecraft telecommunications, but it is quantitatively different: it uses frequencies of 7.25 to 7.75 GHz for uplink (Earth to spacecraft) and 7.9 to 8.4 GHz for downlink (spacecraft to Earth), as summarized in this Wikipedia article.
Ka-band uses much higher frequencies, 34.2 to 34.7 GHz for uplink and 31.8 to 32.3 GHz for downlink, summarized in this DSN publication.
Since the frequency of Ka-band is roughly four times that of X-band, the wavelength of the Ka-band signals is about one fourth that of X-band. Standard antenna theory (tutorial here) tells you that the angular width of the main beam radiated by an aperture antenna (e.g., a "dish") is proportional to the signal's wavelength divided by the dish's diameter. The signal intensity at the center of that beam is proportional to the inverse square of that ratio.
So for the same size dish and same transmitted power, a Ka-band system can radiate a signal with ~16 times the intensity of an X-band system. However, Ka-band receivers have higher noise figures (this paper; and multiple DSN/Descanso publications ... but look out, they're hundreds of pages!), so the net gain in data rate is about a factor of four. Not too shabby for no increase in power transmitted and no increase in antenna diameter!
Drawbacks to Ka-band
With a narrower main beam, the antenna must be pointed more accurately, and this might drive a spacecraft's pointing knowledge and accuracy, making the attitude determination and control system more expensive.
With a shorter wavelength, the accuracy of the dish's surface shape must be better, usually meaning that the dish will be more expensive to build.
Shorter wavelengths are more susceptible to inclement weather (Reference here, but watch out, it's long and not for the faint-hearted!), so rainstorms that would only mildly affect an X-band system can bring a Ka-band system's signal strength below the threshold needed for the data rate being received on the ground, and you lose the data. This is the crap-shoot: if you go to Ka-band, on good days you get much more data than you would at X-band, but on bad days you get nothing.
Despite these potential drawbacks, the gain in available bandwidth is significant, and NASA is going whole hog for Ka-band telecom with its deep-space craft.