There is no single DPS number that I have seen (only about 45 minutes play time), much like Borderlands. Instead, you've got to look at multiple stats and make a judgement call based on personal preferences. As with Borderlands, I expect that taking things for a spin will be really important when it's a close call.
In addition to the stats you see when you mouse over a weapon, there are at least a few hidden stats: Zoom Level (present in Borderlands 1), recoil, and stability. Shooting down a sight impacts DPS, obviously, and stability is a major factor there. Recoil will affect dps when firing rapidly/burst.
It's not always desirable to shoot as fast as possible (even when not using scopes/iron sights). I think it's just impractical to include a DPS calculation. I do wish Borderlands weapon "cards" showed more stats though. Stability is really important for sniping, for example.
Your Badass Rank is a universal stat that applies to all of your characters, and all of your characters contribute to your rank.
You get Badass Ranks from completing the challenges outlined in the Badass menu (default J on pc). You can see these challenges in a list on the right-hand side. Some challenges are tiered, and reward you with more and more Badass Ranks and customization items as you advance up in tiers. Some challenges are one-off and provide a one-time reward. You can complete a challenge once with each character, which effectively allows you to endlessly increase your Badass rank as you create more characters. You can also track challenges by clicking on them in the list.
You get more Badass Tokens as you accumulate Badass Ranks. The current rate is unknown, but is estimated to be:
Badass Rank = (Badass Tokens)9 / 5
Rounded down to the nearest whole number (source).
Badass Tokens can be spent on a set of 5 random upgrades. Each upgrade can be purchased multiple times to no maximum, but there are diminishing returns. For any one upgrade that you invest in, the total accumulated magnitude of that upgrade is given by:
Magnitude = (Badass Tokens spent on option)3 / 4
This means that if you invest 20 Badass Tokens to +% Gun Damage, you will have ~9.5% bonus gun damage on all of your characters (source).
Customization items are unlockables you can use to customize your character head and body skins/colors.
On request: here are the steps to calculate how many Badass Ranks you need for your next Badass Token:
- Calculate your current expected Badass Tokens from your Badass Rank.
- Calculate the expected Badass Rank for an additional token.
- Determine the difference between the expected rank and your current rank.
Expected Badass Tokens = (Current Badass Rank)5 / 9
Expected Badass Rank = floor(ceil(Expected Badass Tokens)9 / 5)
Ranks Needed = Expected Badass Rank - Current Badass Rank
For example, if you are at Badass Rank 1000, you have an expected 46.41 Badass Tokens (meaning you have 46 available). For one more token (47), you would need about 1022 Badass Ranks, meaning you will need about 22 more Badass Ranks before you get another token.
Best Answer
Note; I have not played through the DLC, there might be some changes that occur in them that I am not aware of.
With that said, If you go to the Eridium Black Market (Crazy Earl's shop in sanctuary), you'll notice all the SDU upgrades are categorized as "Upgrade". The ammunition vending machines having a filter for upgrades is probably a holdover from the first Borderlands game where ammunition SDUs were purchased from these machines.