Roughly speaking, the differences are:
Dolby Vision is effectively 12 bit while using only 10 bits for encoding the actual signal. HDR10 is effectively... 10 bit. To achieve the same 12-bits of dynamic range they'd have to come up with a HDR12 format or something.
You can think of 8-bit SDR brightness as something like 0 nits to 255 nits of brightness. This is technically wrong because it's a nonlinear curve, but ignore that for a minute. Increasing this to 10 bits like with HDR10 gives you 0..1,023 nits with the same "steps". Going further to 12 bits lets you take this to 4,096 nits while continuing to preserve the same level of gradation.
The hiccup with this is that some displays have 600 nits of peak brightness and some have 2,500 nits. There are rare displays that can go to 4,000, and prototype displays that go to 10K nits.
HDR10 only goes to 1,000 nits.
Dolby Vision goes to 4,000 nits.
Does this matter now on some cheap LCD TV that only goes to 600 nits? Probably not.
Does it matter on an OLED panel that only goes to 1,000 nits? Maybe, because Dolby Vision has more true-to-life mapping from the maximum range to the display panel range.
Will it matter more with next-generation panels capable of 3,000+ nits? Almost certainly.
Then again, HDR10+ has dynamic metadata, which compensates a lot for its lower bit depth. Additionally, most smart televisions smooth the "steps" in smooth areas, largely eliminating the artefacts caused by HDR10.
At the end of the day, they're both significantly better than SDR, but Dolby Vision is a touch better, especially on high-end panels.