I am not an expert in this so I hope someone will correct any mistakes I made. This is not supposed to be a top level comment, but there are no other comments here at this time.

Moving on. It's hard to answer such questions because:

1. Religious beliefs change over time so it becomes a definitional thing rather than an exact science how much the belief is allowed to change before you call it not-Judaism or not-Hinduism.
2. It's hard to separate historical fact from fiction, because both these religions have extensive myths about their origins, and many of the events cannot be substantiated independently.
3. It's hard to date very old events accurately. Even the oldest written records existing today are copies of copies of copies; the originals are not available to be dated. So you have to date them by other means such as linguistics or putting them in the context of other, known events. This kind of dating is often imprecise and can give you a range of a thousand years rather than a specific year.

For example, textual analysis of the Torah (first five books of the Old Testament, the oldest part of the Bible) seems to indicate multiple authors, spread over a period of several centuries. The oldest of these sources is hypothetically dated to about 950 BC. In comparison, similar textual analysis of the Rig Veda indicates that it was composed between 1700 - 1100 BC, making Hinduism the older religion.

But the traditional view of Judaism is that the Torah was written by Moses himself. There is no historical evidence of Moses that I am aware of. Biblical chronology seems to place him around 1200 BC, which is possibly the same age or older than the Rig Veda. But this doesn't seem like a fair comparison, because one is based on the religion's own mythology, while the other is based on modern textual/linguistic evidence. Similarly, if you were to take Hindu mythology at face value, the Ramayana was composed around 5200 BC and the Mahabharata around 3400 BC. But I don't believe many scholars take these dates seriously. In Judaism, you could similarly point to stories about Abraham and date him using Biblical chronology to 2000 BC, but there is no evidence outside the Bible at all that suggests that even was an Abraham.

Looking at it from the perspective of culture doesn't help much either. Cultures change too much over time to maintain that this culture today is the same as the one it originated from 3000 years ago. You can't really do that without stretching definitions until they become useless.

The earliest mention of Israel or a people known as Israelites in the archeological record is the Merneptah Stele dating from about 1200 BC, which describes the Pharaoh Merneptah's conquests, and contains the line "Israel is laid waste". There is some controversy whether the word is really "Israel", with some scholars saying it's Jezreel and others saying it's just a generic word for nomads. But assuming it's true, you have a people relatable to Judaism at 1200 BC in the Levant.

Similarly the Vedic Sanskrit speaking people who composed the Rig Veda were living in the Indian subcontinent by about 1500 BC, or possibly earlier.

Then there is the question of the religion itself. The practice of Judaism didn't really become uniform or codified until the Babylonian Captivity, at the earliest (around 600 BC). Prior to that, archeological evidence shows a lot of variation, including the worship of multiple gods (which is certainly against monotheistic Judaism). It would be hard to defend that the Judaism practiced in 1200 BC (if indeed the people mentioned in the Merneptah Stele were Jews) was the same as that practiced when the Dead Sea Scrolls were written, a thousand years later. Some elements remain common, but much of the religion has changed.

Similarly, you could make an argument that the religion of the Vedic people wasn't quite Hinduism. In fact, scholars make a distinction, calling it Vedic or Ancient Hinduism, versus Classical Hinduism that appeared around 600 BC. Many of Hinduism's core beliefs such as reincarnation or karma didn't appear until then. But there is a continuity too, the Rig Vedic gods are prominent in the Classical Hindu pantheon, Rig Vedic practices such as yajnas are still carried out today, the Rig Veda is still a sacred Hindu text.

Then there is the question of even older sources. There is some evidence that Hinduism may contain elements of the Indus Valley culture. For example, the Pashupati seal seems to show a deity sitting in what looks like a yogic posture, with cattle horns on his head, surrounded by animals. There is even a hint that he might be 3-headed, with marks on the side of his face that look like orthogonally projected faces in profile. This is very much characteristic of the Hindu god Shiva, who shared these features. But you can't really draw conclusions from perceived resemblances, and many scholars dispute this interpretation as well. But if true, you could extend the source of Hindu beliefs another thousand years earlier. This is not the same as saying that Hinduism is that old, just its origins.

So I don't think it can be definitively said which of the two is older, it becomes a matter of definition, further confounded by hazy dating. By some obvious measures (such as dating the Rig Veda to 1100-1700 BC and the Torah to 950 BC, or by dating the Israelites to 1200 BC and the Rig Vedic people to about 1400-1500 BC), you could say the estimated dates for the origins of Hinduism appear to be somewhat older. But that's a long way from saying Hinduism is older. I think modern religions are really modern constructs, none of them is more than a few hundred years old if you want to maintain meaningful similarities. That goes for both religion and culture.