I suspect that the next PlayStation console, the PS5, will have the biggest relative jump.
First, I do not think that Sony is going to release a proper Vita sucessor next generation to compete with Nexus or whatnot. The Vita has had enough trouble that it would make more sense for Sony to focus on console games and possibly some mobile stuff for other companies' hardware.
Now, the 9th gen will probably start with Nintendo. The 3DS been out for over 4 years, the Wii U has been out for a year longer than the PS4 and X1, and Nintendo would likely benefit from putting the Wii U behind them. Now, we don't know that much about the upcoming NX, but it will probably released in 2017 based on the expected mid-2016 reveal. NX is speculated to emphasize a high degree of cross-compatibility between Nintendo's handhelds and consoles, to the extent where they share many games. This would coincide with Nintendo's careful steps in this direction, like Super Smash Bros 4's dual platforms, NES Remix, Mario vs Donkey Kong, and so on.At very least, the console version of NX would need to be compatible with most handheld NX games.
Thing is, cross-compatibility implies that the console and handheld versions would need to have a lot in common, meaning the handheld could easily hold back the console. And honestly, I don't think Nintendo would mind that much. One of the Wii U's many problems has been the priced of the console, and even a couple of years later it is not that much cheaper than the competition. And because Nintendo will enter the 9th gen in 2017, it will likely be competing with the Xbox One and PS4 with significant price cuts, possibly at around $300 or so for a standard bundle. At very least, Nintendo will not want their next console to be notably more expensive than the Wii U launch price of $300 and $350. This implies a much smaller jump than the Wii U had over the Wii, though still a bigger jump than the Wii was. Nonetheless, it will still be a relatively small jump.
The NX handheld will probably receive a bigger jump from the 3DS than its console counterpart does with the Wii U, but I am not sure how dramatic this jump will be. Nintendo has generally done better when its handhelds are relatively cheap, with the 3DS launch showing how even they could mess up. Price would have to be a touch higher than preferable simply to support the same basic hardware and/or OS ans the console version, but $250 would still be the borderline barring some amazing killer app. The good news is that mobile tech has likely advanced enough so that the NX handheld can be fairly powerful despite its size and price.
After Nintendo, Xbox's 4th incarnation is the next likely new challenger. Sony will want to profit from its successful and increasingly cheap PS4, but Microsoft would wnt to replicate the phenomenon where the Xbox 360 became the standard for multiplatform titles by coming out a year earlier. I suspect the 4Box will come out in 2020, seven years after the X1. The 360 lasted a full 8 years, but Microsoft's initial troubles with the One will likely push them to release new hardware sooner, especially if they can't make a mid-genlife extension like Kinect was in 2010. This hardware leap will likely be comparable to the PS360 to PS4/X1 leap, so a moderately large one.
Sony is not going to want to retire the PS4, and could easily influence European markets enough to make the big generation leap slow down until the PS5 is ready. Japanese developers would likely still make games for it as long as they're supporting the NX. So the PS5 will likely come out in 2021 or 2022, 8 or 9 years after the PS4. I think that extra year or two will give the PS4 an edge over the X1. And technically speaking, it will be a huge jump. For scale, there was a 9 year gap between Sega's Master and Saturn consoles and a 10 year gap between the GBA and 3DS.
tl;dr: PlayStation 5 > 4box = NX Handheld > NX Console
Love and tolerate.
