Actually both can drop all the things you mentioned (apart from the second generation pearls), but you tend to get runs of the same types of gear from any given source. Switching things up from time to time is always a good plan - keeps you from getting bored, mainly!
I think I’ve gotten at least 1 of every second gen pearl as well as at least 1 of each first gen pearl. I’d say I have more Storms than anything else with Bekah second and Butcher a close third. The only weapon/unique item I haven’t gotten (aside from the gemstone variants) is the Hawkeye- it’s still on my bucket list…
Color me, and I’m sure lots of other folks reading this post, jealous. Like eighteen shades of jealous. Your tales of bountiful, shiny loot goads us all to get back into the fields every day. 
(That may be a little over-the-top, but it’s not entirely facetious. Posts like yours are what have me running around like a madman on Pandora. There’s pearls in them thar hills!!!)
I’ve got piles of legendaries and 1st gen pearls from mostly the LLMs and a couple from Tubbies. My last couple attempts at the LLM’s at WEP have given me nada except for a shield I didn’t want. A WTF shield if I recall correctly.
Of all the pearls I’ve gotten, I don’t use a single one. I had high hopes for the Storm, but I’ll probably never use it. The Sawbar was fun, but I’ve not used it once since goofing around with it right after getting it. I’ve heard good things about the Avenger so I may need to take one of those for a spin (have 3).
I’ve never heard a bad review of the Bekah. I understand it has a learning curve to use it to it’s full potential. It is probably the only gun I might take as a trade or whatever (I like to farm my own stuff). Not gonna get my hopes up on that.
Last night I did several runs through Bloodshot. My first run was terrible, I didn’t die but it was just sloppy and went into FFYL several times.
Between runs I did some of my other routine farming runs.
I set some rules for myself. If I die, I start back to the front of the map. I also came up with tactics in regards of how to deal with specific enemies.
At some point during one of the latter runs, things improved tremendously. I started to play a little more aggressively and gained some confidence. My last run of the night went very well. I felt like I was in “the zone”.
For the last couple runs I only allowed myself to use the Slag Pimp and the Purple Jacob snipers. I have also decided that I prefer the Skookum prefix for both the Muckamuck and the Callipeen.
I’m certain that the Muck is the more powerful gun but somehow I seem to get better shots with the Callipeen. I don’t know, I’ll keep em both. Right now they are my favorite guns.
I also upped my controller sensitivity settings per Prismatics suggestion. I ended up going up 3 on both X&Y. I did it gradually between runs. It definitively is an improvement.
Also bumped my FOV up in the Video Settings. Another positive change.
Next map I’ll tackle is Southpaw…then Sawtooth.
That might have to do with the parts you have on them. Muckamuck has additional recoil. Callipeen has regular or even reduced recoil and better recoil recovery depending on which barrel it has on it. The other parts can also change recoil for better or worse. If your problem with Muckamuck seems to be centering it again after shots I’d bet that’s where it all comes from.
That’s what I prefer too. Jakobs already focuses on pure damage output so pouring some more of that on it feels good.
I tend to see Storms where ever I go. Definitely the most common one for me. I’ve seen it in several chests, Marcus is hellbent on giving it to me as a Merc day gift and once it even came out of a hanging Stalker goopile or some other excrement I shot on my merry way.
I mentioned that I prefer the Skookum because I had previously said I prefer the Klook Callipeen due to it’s reduced recoil. I’m finding, however, that recoil isn’t posing as much of an issue as I thought it would. In the heat of battle I’m not really even noticing it like I am in a controlled environment. ie Shooting walls vs shooting ironclad lunatics charging you screaming about meat monkies …
Right now I’m just trying to learn to use the guns effectively and also decide which would be best as part of my default load out. It seems silly to have both.
I also played a bit with the Striker on the same map. I’ve never been much of a shotgun player but it worked for me surprisingly well.
I’ve actually had 2 so far. One was under leveled so I sold it. Not sure why I’m keeping the one I have now. I’ll likely never use it.
That said, in the past I’ve gotten rid of items to find later they would come in handy for a specific purpose. For example: If I didn’t plan on shooting Pete’s face off I wouldn’t keep lugging that Trespasser around.
I will conclude that we all agree. Storm’s have a good drop rate. 
Its really not a good “pop some heads with crits” sniper rifle. If you ever decide to roll Gaige with a focus on elemental DOT you may find it useful. She can really pump up that shock damage to pretty dangerous levels.
And this is why I keep EVERYTHING…well, within reason.
They are very few, if any, pieces of gear that are just plain unusable. Point in fact, the WTF shield gets a lot of hate, but I love it (at least in open spaces, indoors it’s as bad as the skyrocket nade, if not worse). I use it on Axton. I toss out a couple of turrets, hang back and pick off unfortunate enemies that give me a chance while the boosters strip shields for me (and outright kill stuff when I rock a shock bone). Come to think of it, Catalyst Gaige would probably get some good use out of it too. That just went on the To Do list.
Ey!
Hate on something else, I propose the Wonderlust.
I like the wanderlust. It’s not half bad on maya
No hate here. I love the skyrocket nade. I was only talking about indoor use, and I use it then too, albeit very cautiously. I give everything a fair shake, and if I can’t make it work for me I still won’t hate it altogether.
Or cheese him under the pipe. 
Looks at his 55 mules Define ‘within reason’ 
I did see a video that involved getting Slappy to spawn, having to climb the ladder, then cheesing him from a spot he can’t hit you. That takes too long for me. My method can get the job done in seconds most of the time. There are a couple times he puts me in FFYL, and there are rare times I kill him and he still manages to put me in FFYL before he checks out and I have no recourse.
Whoa…I have about a dozen mules and I’ve been working on organizing them better. I don’t keep duplicate or inferior items most of the time. Chest farming the Torgue DLC the past couple days I’ve gotten a Lyuda that was inferior to my Gromky, and a Sham that is identical to one I already have. I don’t keep that stuff.
One thing I curious about is leveling up mules. I’ve seen post where folks will say they do this. All my mules are lvl 1 and used strictly for storage. I just learned yesterday that even lvl 1 can purchase backpack upgrades and use the bank at sanctuary. If I don’t plan on using mules to play why level them up?
The two possibilities that come to mind are:
- They don’t have access to split screen so getting a mule to sanctuary and buying storage upgrades is a desirable thing.
- The just want a new character to play so they use their mules.
I’ve never been one to use mules excessively, and most just got forgotten so I’m sure others will have other reasons for leveling their mules.
yes, that makes sense.
I can see this happening. I don’t expect that I will use them much more.
In other news I’ve still been playing through Bloodshot and my runs are getting much better.
I also did the mission to receive the Heartbreaker. Oh man, I do love that shotgun. I can forsee it being used very frequently.
So my next map to start practicing is Southpaw. I’m also thinking about farming the Kitten…and then I’m going to reset and restart the playthrough of the main game.
When I do reset, I will probably do the Torgue DLC first as another goal of mine is to farm Pete without cheese. I have been working on that off and on, and I’ve gotten close…but still can’t quite get it. I will though.
PC players are hard to find! I might be interested!
I’ve been asking myself the same question and only answer I can find is what @Prismatic said:
Don’t have access to split screen
Always been a … “bit”
if a hoarder… Enough to get the "Can’t create more saves.) on PS3. The the “55” number I think. It included some regular characters thou. Some.
Some items (very few) only have a sentimental value. Like that green “pure Hyperion” Sniper… I used it!
Way too many fall in the “might be useful at something one day” category. A pain overall but you do save on farming time. Not such a big need before UVHM I found out. It did saved my rear end on a few occasion.
One positive thing was being able to choose and decide when to do the “mandatory” dlc’s (parts).
With all classes soon to be leveled to 72 a bunch will be move to some kind of digital archive to be forgotten. Hopefully! 
With split screen on PS4 requiring to use an alternate account I found myself moving some to Sanctuary. To have access to both Vault and New-You stations in the same area.