Well, clearly this is all a matter of subjective opinion, and I thing by my signature line you'll know where my loyalties lie!

When I set about on my current double eagle obsession, I chose Saints mainly because it had been a dream of mine to own just one ever since I was a kid just starting to collect. That evolved into pursuing a set, and as that process has unfolded, it has become clear that the Saint-Gaudens eagles and double eagles represent what many would describe as the absolute pinnacle of United States coin design. When Teddy Roosevelt looked at his change he saw Longacre's designs that were more than a half century old compared with the more beautiful designs of ancient coins and those of contemporary Europe (I shudder to think what Roosevelt would have thought of today's monstrocities!). So in 1907 with the introduction of the two new Saint-Gaudens designs, TR ushered in a new era in coinage which eventually brought us the winged liberty head dime, the standing liberty quarter, the walking liberty half, the peace dollar, the buffalo nickel, the incuse indian half and quarter eagles, and a hairs breadth from having a Saint-Gaudens cent (unfortunately we ended up with a century of Lincoln). Everything since this golden age has been one step after another toward bland lifeless basemetal tokens for our coinage. So this is a major factor in my preference for Saints.
Despite my obvious preference, there is one area where Saints fall far short of Longacre's Liberty, and that is history. Unlike the Liberty design (particularly the early coins), Saints seldom circulated, as most sat in bank vaults as backing for various currency notes. Some dates did circulate, such as the early dates from 1907-1916, and some random dates like the 25-S, but by and large the coins were not used in commerce but as a reserve asset. Liberty double eagles, particularly Type 1 and 2, circulated heavily and were a major part of commerce in the 19th century. From the initial coins of the gold rush era, through the Civil War, all the way through W.J. Bryant's cross of gold speech, these coins served as currency. Granted, they began to decline in use once a stable system of currency notes was established after the Civil War, so many later Type 3s circulated about as much as Saints, but the history in commerce is impressive. And of course I own a number of Liberty double eagles, and the design is pleasing. I prefer the original Type 1 to the subsequent modified versions for its simplicity and clean lines on the reverse. And certainly when I hit the wall on Saints (in about 3 or 4 more coins!) I will likely start a set of Type 2 Libs, as they are almost perennially ignored in the market, so lots of bargains to be found, particularly in AU-55 through MS-62.
Those are my rambling thoughts, great topic for discussion!