I have a Bulga butterfly tote and a Moni Moni Splendor. While the Moni bag is soft, it's not nearly as soft as the Bulga. They're entirely different types of leather.
Bulga is like a soft sheepskin (at least that's what I was told when I first bought one), and it definitely gets softer the more you use it (I also think the bag had more of a matte finish when I first got it, but is now a little shinier). The color is pretty even throughout and the bag wears well, altho the leather can be a little more delicate & rubs are more apparent.
The Moni is a washed leather and the leather is inconsistent throughout. Some places the leather's softer than others, and the color tends to be uneven (like a faded pair of blue jeans). I find the leather on the "hidden" pocket (underneath the front pocket of the bag) is very tough, and the backside of my bag is softer than the front. I haven't had it that long, or used it that often, so I don't know how much more it will soften (but from what I understand, the leather will continue to soften up). I like the size & shape of the Moni, and it holds a lot more than I thought it would. I also like that the longer shoulder strap can be worn cross-body. Because it's made of washed leather, wear isn't as obvious. Scratches & scuffs probably aren't as obvious since the bag is supposed to have a worn look.
Both bags have their pros & cons - I guess it comes down to what's more important to you. Do you want an extremely soft bag, or one that's a little tougher.