For argument sake, what sort of damage can Nidalee put out at Level 6? I would assume she would land a spear (we'll claim the 200% damage cap) and follow that with pounce, takedown and swipe. Figuring three ranks in Q, her spear lands (100 + 40% AP)x(2). Figuring she has taken AP masteries and runes, she might have roughly 30 AP even before items. She just might have one completed item at this point, but I doubt it. More likely it will be a Doran's Ring and NLR (75AP) or just the Runeglaive (50AP) for those junglers. So either 105 AP or 80 AP at level 6.
Mid Laners Spear is capped at 284 damage. Junglers at 264.
Quick compare, Lux hits her rank 3 Q with the same items and it will do 230 damage, regardless of range. Annie's rank 3 Q also does 230 damage and cannot miss.
However, Nidalee has three more skills to burst you down compared to other champions.
Her pounce at Level 6 (rank 2 cougar) will add another 100 + 30%AP. Even if she hit you with a half range spear, she has made up for the lost damage with pounce. Midlaners 132 damage. Junglers 124 damage.
Takedown naturally comes next, which will get a 33% increase for being marked. Takedown base stats are 20 + 75%AD + 36% AP. Figuring neither Nidalee iteration will have any additional AD, she has a natural AD of 62 at level 6. Mid Lane Nidalee will strike for 139 damage and Junglers hit for 127 damage.
This will be the major departure though between Mid and Jungle. Jungle should have Runeglaive, which carries a Spellblade that should land with the next AA. Mid is going to deal out a meager 62 phys damage with an AA while a Jungler has a 100%AD + 30%AP boosted AA. Jungler will wallop you for another 148 (that added 86 damage easily makes up for all the small advantages Mid laners had to this point).
At this point, pure damage dealt from Mid Lane Nid is 617 damage while Jungler Nid dished out 663. These are maximums with the minimums hovering around 475 and 531 respectively (half range spears). Of course your armor and mr will reduce this damage, but these numbers can be used to compare with other burst mages.
Oh, but I'm forgetting Nidalee can easily get a Swipe in and probably pounce you again. Swipe does 130 + 45%AP regardless of whether or not a target is marked and has fairly decent range even if the target started to run. She could also toggle back to human form to land a close range spear, which resets her cougar form and allows her to dive right back into her combo.
It's a wonder why I do so poorly with her with all this damage she can dish out.
Oh, no it isn't.
Because Nidalee doesn't stun or CC you at any point of that mess. Her only real defenses at this point are base stats, runes and masteries. While she is bursting you down, you can burst her back. If you have any stun or CC to interrupt her chain, you'll probably end up ahead. Just compare the numbers.
Nid pounces on Lux. Lux will probably Q, Flash (out of melee range), R, AA, E, AA. Her cooldowns won't let her do much more than that.
230 (rank 3 Q) + 375 (rank 1 R) + 82 (passive+AA) + 120 (rank 1 E) + 82 (passive+AA) = 889 raw damage.
I don't think it would be too hard for Lux to hit her Q at short range, so this combo should be a valid counter that forces Nid to flash and retreat.
IMO I think Nidalee might be a bit weak for Mid Lane. As a Jungler, she seems to be fine picking off unsuspecting targets under 50% health. No different than any other jungler.