The Coen's regular DP, Roger Deakins, prefers shooting with spherical lenses, cause, among other things, he often shoots at very wide apertures, likes to use shorter focal lenghts and dislikes the optical aberrations inherent to anamorphic lenses. As many other great DPs famous for their use of natural light (John Alcott and Néstor Almendros come to mind), Deakins may find difficult to shoot in available light or very low-light levels in anamorphic, because (i) anamorphic lenses tend to be slower than spherical lenses and (ii) the depth of field is very shallow when shooting wide-open in anamorphic, thus making focus very critical. But Roger Deakins still admits he has discussed with the Coens in the past about shooting anamorphic for a certain project that fell apart, so it still depends of the style of each picture. For instance, in 1976, it would have been imposible to shoot "Days of Heaven" in anamorphic the way it was shot, as back then there were no anamorphic lenses opening up to T/1.1, and wide apertures were a need to achieve good exposures of the magic hour shots as non high speed film stock had been developed yet.
Technically, 35mm anamorphic uses a bigger part of the 35mm negative than Super 35mm cropped to 2.40:1, thus the images tend to look richer, crisper and less grainy, in equal conditions (light, weather, film stock, etc). But again, some anamorphic lenses are old designs and the images could end up being softer than those shot in Super 35 with the newest spherical lenses, such as the Zeiss Master Primes, or maybe these anamorphics need to be stopped down at least to T/4 or T/5.6 to get a decent depth of field or good quality images.
Malick's now regular DP, Emmanuel Lubezki, is close in style to Deakins or Alcott when he's working with natural light, so he's probably more confortable using spherical lenses that open up to T/1.3. Prior to "The New World", he had only shot a picture in anamorphic ("Great Expectations") and claimed in interviews how unconfortable he felt working with Panavision's Primo anamorphic lenses. So I guess he would have preferred to shoot "The New World" spherically and finish it with a Digital Intermediate, but was convinced by the director to try anamorphic again, to finish it photochemically, to shoot in available light and use deeper T stops to get a lot of depth of field, which is as hard as it can get. Lubezki did a remarkable job, and now probably Malick is more confident on his capabilities and lets him choose the shooting format, or it's just that testing has conviced the duo that Super 35 fits their needs better than anamorphic for "The Tree of Life", if they planned to use a lot of natural or available light. We will see!