The primary “advantages” of 2 panel saddles over single panels include:
Modularity—position and comfort can be adjusted across a broader scale. Panels can be overlapped, slightly overlapped, slightly separated, or separated far apart.
Comfort—yes comfort gets its own category. Not saying they are all unequivocally more comfortable than single panels because not all two panels are made alike, and some single panel designs are favored for their comfort among their users (e.g., cruzr xc, dryad, etc).
However, one distinct advantage is that some models offer more 2” webbing pieces in the saddle design than single panels. This helps distribute the load more evenly without a material that stretches over time. Nutterbuster and others have discussed this in greater detail.
Smaller footprint—designs like the recon and method 2 are designed to overlay on the walk in for a more streamlined walk through the woods. Essentially, this reduces sagging or floppy material hanging off your waist. Only an advantage really for those who prefer to wear their saddles in (vs packing them in).
Now, for the disadvantages:
These vary based on model/design as each saddle may have its own quirks.
Fiddly—the trade off with extra adjustability is the extra time and effort to situate the panels in a preferred position. For the most part, you just sit in single panels. 2 panel saddles requires moving each panel around. For the recon (which I love, despite its “quirks”), it can be fiddly for a few seconds separating the two panels or getting them back to a perfectly overlapped position...really not a big deal, but perhaps worth mentioning. The method 2 reduces the hassle through their design and use of a magnet system.
May not suit all climbing methods—some may prefer single panels for certain climbing methods but I use sticks, steps, and bolts so it’s a non issue for me and my two-panel. Some guys love 2 panels for one sticking and others prefer pleated single panels. SRT or DRT folks seem to prefer pleated singles also (in general).
For the record, I started with an aerohunter kite; I now hunt with a Treehopper recon. It is more fiddly at first but the trade offs are worth it. I can move both panels under my butt and gain extra mobility/bow clearance or I can raise the top panel up for back support. To me, the recon is noticeably more comfy, although it takes a few extra seconds to find a sweet spot. With the kite, I would be comfy for a short while but it would constantly ride up on me, requiring me to move around a lot and “fiddle” with its position.
I am not even tempted to look back at a single panel. Hope this helps.