In most scenarios, our bodies respond to training stimulus very specifically. This is called specific adaptation to imposed demand, which tells us:
specific skills or training may not easily generalize or transfer to distinct activities.
You might be lifting more in the bicep curl, but curl strength doesn't necessarily translate to pull-up strength. (Of the two, I'd say that pull-ups, being a compound exercise more applicable to real-life tasks, would be the better metric of strength overall. My understanding is that they use more of the back, abs, and shoulder girdle.)
In light of your update, this also means that it's likely that you adapted to pull-ups with a specific grip.
It's not the bar. It's you.
Henry Rollins brings the truth in this domain with his essay, Iron and the Soul:
The Iron never lies to you. You can walk outside and listen to all kinds of talk, get told that you're a god or a total bastard. The Iron will always kick you the real deal. The Iron is the great reference point, the all-knowing perspective giver. Always there like a beacon in the pitch black. I have found the Iron to be my greatest friend. It never freaks out on me, never runs. Friends may come and go. But two hundred pounds is always two hundred pounds.
You might be able to do more tricep cable push-downs than before. You might have look better, feel better, and have better body composition than when you were doing ten pull-ups. But two hundred pounds is two hundred pounds. If you can't do 'em, you can't do 'em. Don't blame the equipment, blame yourself.
But it should be a good blame--a heartening aiming of responsibility at oneself. Because as those who train know, we can tell our bodies to do things, and our bodies will respond. If you do more pull-ups instead of isolation exercises like curls, you'll be able to do more pull-ups. I'd suspect you'd be able to do heavier curls, too.
That being said, if it's your grip that's failing, then yes, it could be the thickness of the bar that's affecting your pull-up numbers. Thicker bars are much harder to hold on to, and so provide excellent tests of (or training for) grip strength and endurance. (NB: the OP's update suggests this to be the case.)
Or perhaps when you were cheating more on your pull-ups before. Not extending your arms fully, not getting all the way to the top, and kipping up to the top could all explain a difference of several reps. But I'd hope you're doing dead-hang strict pull-ups both then and now, which would allow you to legitimately track your progress (or regress).
If the goal is strength or ability (rather than appearance), it's important to pick exercises carefully so that they have maximum carryover to other exercises. This is what leads us to squats rather than leg presses, or pull-ups rather than curls, or deadlifts rather than machine exercises for the back. These are highly demanding compound exercises that carry over well to general strength and sport. The question is, what is your goal? If it's more chins, then do more chins. If it's heavier curls, then do more curls. But if it's general strength, then I'd advise the chins over the curls.