Most of this information comes from Saxton Pope's Yahi Archery and The Traditional Bowyer's Bible, which is a book on construction methods and not a historical text. However the series does contain a fair number of subsections dedicated to the history of particular styles and construction methods, so in the absence of other more credible sources I offer you what I've learned from the series.
As far as North American First People's bows go, there were an incredible number of different styles of bow. The basic summary is that different cultures had different bows, and there were different bows for different purposes even within the same cultures.
For instance, bows of the Eastern woodlands tribes tended to be what's called a 'self bow', which is a simple bow made from a single piece of wood, typically with a flat cross section. Recurves were uncommon but not unheard of. They were shaped out of a stave that was hewn and aged, then tillered to shape. Typical woods used were osage orange, black locust, mulberry, sassafras, hickory, ash, cedar, elm, dogwood, birch, walnut, oak, etc.
Length varied by purpose of the bow. War bows tended to be longer to store more energy (war bows tended to have much higher draw weights), while hunting bows tended to be shorter for ease of handling in the woods.
Among present day Cherokee bows, there appears to be two distinct length: a long bow of about six feet and a shorter bow of about five feet. Today, the longer bow is preferred for the long-range sport of cornstalk shooting, and the shorter bow is preferred for hunting since it is easier to use iin brush. The longer bows are often of heavier draw weight, 60 to 80 pounds or even more, while the shorter bows usually draw about 45 to 55 pounds.
I believe these two types of bows reflect aboriginal types which have been handed down from the pre-Columbians to the present day. The longer bows were used by the early Cherokees primarily for warfare while the shorter bows were mainly used for hunting
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The longer bow, which I refer to as the 'war' bow, is usually close to six feet in length and rectangular in cross-section. There is no handle section, and the widest part of the bow is in the middle. The bow bends throughout its entire length in a smooth arc, like the letter D, from which comes the name D bow.
[...detailed dimensions of the bow are here...]
The shorter bow, which I refer to as the "hunting" bow, is generally about five feet in length. The illustrated bow is also a D bow with rectangular limbs and no handle section.
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The Cherokees, and other Eastern Woodland tribes, also made another type of bow besides the D bow, which I refer to as a handle bow. These had a non-bending handle section a few inches long which was normally narrower and thicker than the maximum dimensions of the working limbs. The Sudbury bow, which we previously examined, falls into this category.
- The Traditional Bowyer's Bible, Volume 2, Chapter 3, Eastern Woodlands Bows
Here it's worth noting that Chapter 3 of Volume 2 of the Traditional Bowyer's Bible was written by Al Herrin, of Cherokee descent and raised in the traditional way, and the chapter contains many descriptions of drawings of bows and arrows from various Eastern tribes. He also has a section titled "What are the sources of information about pre-Columbian Bows?" which sounds like it's right up your alley.
Moving away from the Eastern Woodlands, most historical descriptions of the "plains bow" was as a sinew backed (the outer surface, which faces away from the archer, is laminated with a 'backing' material, preventing the wood from breaking where the tensile stresses are the highest) short bow that was intended to be used from a horse. However this is post-Columbus, and were not representative of what most pre-Columbian first peoples bows were like. As best we can tell the traditional plains bows were also self bows, but sinew backing was more feasible outside of the moisture and humidity of the East coast.
On the West coast, we have some record from Saxton Pope and his contact with Ishi, the last of the Yahi tribe. Pope mentioned several bows constructed by Ishi. His bows were made from juniper, backed with sinew, and roughly the same length (4 feet and 2 inches). Ishi adjusted the draw weight through the width of the bow, so a war bow was several finger widths thick, while a light hunting bow was considerably less.
Ishi also had a short bow, roughly 44 inches, which it was reported that he shot using a draw similar to the Asian thumb draw. Some of his bows were recurved, which he accomplished by bending with heat from a hot rock. The cross sections of his bow were also elliptical, as opposed to the rectangular or flat cross sections of the Eastern woodlands bows.
It's also an interesting side note that bows of the Inuit were often backed with cable, as the wood they had available tended to be very poor quality driftwood. They came up with an ingenious alternative, which used cables and toggles to provide the energy storage, while the wood just held everything together.
Now, as far as European bows of the same time period, I refer to the conveniently located Chapter 4 of The Traditional Bowyer's Bible, Volume 2, titled "Ancient European Bows" (very convenient).
Neolithic European bows were actually quite similar to the North American First Peoples' bows. Typically they were self bows as well, though they often tended towards wider, flat bows, or bows with cross sections that are D-shaped...flat on one side, curved on the other. Some examples listed in the chapter mention limbs between 1.75 and 2.5 inches wide.
(It's worth noting here that the flat cross section is the most efficient cross section, but the D shaped cross section was popular because it was an easier way to finish the tillering process, which is a quite involved trial-and-error balancing of the limbs and would have been extremely time consuming with primitive tools.)
The main difference here between the Neolithic European and pre-Colombian North American bows is length, many of the European bows were much longer, some of the older artifacts found were quite long (74 inches long for the Meare Heath bow, 64 inches for the longest Holmegaard artifact). This could be for a variety of reasons, including the Europeans being taller than the North Americans, hunting or fighting in more open areas, or that longer bows are less susceptible to certain types of manufacturing defects.
Some of the bows were found with decorative rawhide wrapping, but there's no evidence of sinew being used as a backing material.
By the Iron Age we start seeing a style of Scandinavian bow which we'd now immediately recognize as the English Longbow (the Scandinavians did it first). The artifacts found ranged between 66 and 78 inches long, were made of yew (and some sources indicate fir as well) and had a D shaped cross section. As opposed to the older, flat Neolithic bows these were less wide: one of the artifacts was reported to be 1.1 inch wide and 1 inch deep in cross section at the thickest point.
There's a bit more here, but this turned into a novel and I didn't mean it to, so I'm going to wrap it up.
In conclusion, most of the bows of the North American First Peoples and the Europeans were actually quite similar. They differed mostly in length and the use of backing.
It's also worth nothing that both the North American and European bows were actually fairly primitive compared to the Asian short bows, which were laminated composite short bows and (in my opinion) represent the pinnacle of traditional bow making.