The Long-nosed Leopard Lizard is the bigger animal at normal weights and maximum weights, and it is a lizard eating specialist. Normally, I would favour it pretty easily against a smaller lizard than itself.
However, I think that this is a very close match-up.
To start off, let's look at the skulls:
(Long-nosed Leopard Lizard)
(I know this is that of a common collared lizard, but there isn't much difference in morphology other than size towards the Great Basin collared lizard, so I think their skulls are pretty similar)
I think that the leopard lizard has sharper teeth that will certainly do damage, but the collared lizard has a stronger bite and at these rather small sizes I would find strong bites to be pretty effective towards other opponents. In fact, a smaller collared lizard with a higher bite force will be more successful than a larger one while/after fighting. The collared lizard could use it's strong teeth to bite at the probably rather frail skull of the leopard lizard and try to crush it. If the leopard lizard bites hard enough though, it could do some good damage with it's sharp teeth.
Then there is aggression. Leopard lizards have a bit of a reputation for being quite gnarly and will bite, but collared lizards will commonly fight each other during the mating season. They are very aggressive lizards, here is a video that can show that:
youtu.be/10s-ekJK2VwI am not sure who is the more agile one for now. The leopard lizard seems more lean, and I would have probably given it the agility advantage before, but collared lizards are quick and agile from what I have read. They are also very quick while attacking, the video above shows that.
As I said above (and as the person above me said), leopard lizards are lizard eating specialists and that will make it tough for a collared lizard, but a collared lizard wouldn't shy away from a fight either. A female long-nosed leopard lizard and a male Great Basin collared lizard would be a very tough fight, but I am slightly leaning towards the leopard lizard. Not only is it a lizard eating specailist, but it also has a small size advantage. The leopard lizard would also be pretty aggressive, as I have read before. I think a male collared lizard against a male leopard lizard would probably win though. A male leopard lizard would eat a female collared lizard, though.
All in all, I think the leopard lizard takes this 6/10.