There are many great 4x4x4 speedcube options available, although the depth in great performing cubes is not quite as high as with 3x3x3s or 5x5x5s. There are a few factors to consider when choosing your next 4x4 speedcube:
1. The size
The standard size for a 4x4x4 has shrunk over the last few years, back in 2016, the QiYi WuQue was considered pretty normal at 62mm but now that is a bit bigger than most options, the best 4x4x4s now range from 56-60mm with only a few budget options being larger.
2. The price
Magnetic 4x4x4 speedcubes range from £11 to £30 on speedcubing.org, I don't sell the Gan 460M as it is rubbish but if I did then that would have to be nearly £40!
The bigger the cube gets, the more accurate you need your turning to be to avoid pops and lock-ups, this is a universal problem across all big cubes that actually turn fast, you have to be able to accurately control any speedcube you get or you are going to have issues, it is probably never going to be possible to design a 4x4x4 with universal corner cutting like we see on some modern 3x3x3s.
High end options:
MoYu AoSu WRM - The MoYu AoSu WRM is my main 4x4x4 speedcube and I would consider it to be the best on the market, it is 59mm so is a bit on the smaller side but that is not really noticeable, it is £30 but I do believe its speed and stability do justify that price, it can successfully corner cut a long way and pops are not too common if you aren't going to turn it really roughly.
X-Man Ambition - The X-Man Ambition is QiYi's current flagship 4x4 speedcube, it is slightly larger than the Aosu WRM and slightly cheaper at only £27, it is designed to be a lot smoother and more stable but not quite as fast, it has a light, buttery smooth feeling to it and it is generally more reliable and less likely to pop, although care should be taken with all big cubes to turn accurately.
YJ MGC 4x4x4 - The YJ MGC 4x4x4 is the most popular 4x4 speedcube on speedcubing.org, it is still fast and has a slightly blockier feel than other options, nonetheless, it is still used by many top speedcubers despite being only £16, nearly half the price of the Aosu WRM. It does sometimes have quality control issues so if it feels dry and doesn't turn fast out of the box, I would recommend getting some silicone lubricant such as Pilube Red or Luboss Drive and lubricating the springs, I also offer a Neutrino version for this cube.
QiYi MS 4x4x4 - The QiYi MS is larger than most 4x4x4s at 62mm, it has quite a blocky feel to it but performs somewhat similarly to the X-Man Ambition (it is probably designed by the same person after all), it is only £11 so may be a good entry option but may be too big for most speedcubers.
MoYu RS4M - The RS4M follows on from the RS3M 2020, the most popular budget speedcube of all time, however, it doesn't feel much like its 3x3x3 counterpart, it is 61mm so slightly bigger than most modern 4x4x4s and feels more like the old Aosu GTS2M than the newer AoSu WRM, it has a more matte plastic feel to it, however, it is still a pretty fast and stable cube and can be a great introduction to 4x4x4 speedcubes.
YJ Zhilong 4x4x4 - The ZhiLong mini 4x4x4 is significantly smaller than most options at only 56mm, the same size as most 3x3x3s, it has some similarity with the MGC but does have a different design, it has stronger magnets on the inner layers than the outer layers but still has good corner cutting and performs well.
Ultra budget options:
MoYu Meilong 4x4x4 - The Meilong 4x4x4 is only £7 and does not have magnets but is still a reasonable 4x4 speedcube, it is only 59mm and has a matte feel to it, it is light weight and has a light airy feel to it, however, without magnets it is not going to be as good as the other options available, they did also release a magnetic version at £11 which competes with the QiYi MS.
QiYi QiYuan S2 - The QiYuan S2 is QiYi's £7 budget option, it feels very different to the QiYi MS and has a matte coating to it and a blocky feel, it is bigger than the Meilong at 61.5mm but does still perform similarly well.