Same. In gaming and graphics benchmarks on my 1070Ti over Thunderbolt 3 (Hades Canyon Intel NUC), I've seen no more than a 10%-20% drop in frame rate vs. what I'd expect from equivalent benchmark results reported online, so I'd expect no material difference between PCIe 3.0 x16 and PCIe 4.0 x16 for typical gaming applications, and, from benchmark numbers I've seen, only a modest performance drop from PCIe 4.0 x16 to PCIe 3.0
x8.
This assumes, of course, that the PCIe lanes in question actually exist† and are dedicated to the card, and are not shared with another in-use device via a switch or similar chipset shenanigans.
Case in point: the only time I ever had performance problems with my eGPU setup was when attempting to do 4K HDMI output through a Blackmagic Decklink card while simultaneously using the 1070Ti for compute over the same (shared) Thunderbolt bus in DaVinci Resolve.
As far as I know, this would not typically be a problem with a single-GPU, non-Thunderbolt-connected desktop system, as desktop motherboards typically have at least one full-bandwidth x16 slot, which you'd almost always use for the GPU.
† Physical x16 slots can have fewer than sixteen connected PCIe lanes. For example, while my HP Z820 has four "x16" slots, only three have full bandwidth; the fourth slot supports x16 cards, but only at the speed of an x8 slot, because only eight of the slot's sixteen PCIe lanes are actually connected.