This largely depends on the version, which determines the weapons. Main thing is that the Hind is heavy and large, but can carry troops. The Cobra is light and small, doesn't carry troops, but can operate from an aircraft carrier. I think you started this topic with the Paki Cobra and Indian Hind in mind.
Pakistan
The AH-1F Cobras were acquired in the mid 1980s, of 20 delivered, about 18 remain in service. In 2004 it was reported Pakistan could get about 40 ex-US Army AH-1Fs, but I haven't seen any delivery reports. Armament consists of TOW-2 launchers and 2.75 inch rockets, and the 20mm gun. They've seen action in 2003/2004 against Al-Qaeda/Taliban in the area along the border with Afghanistan.
India
India acquired their first batch of Mi-25s in late 1984. They first saw action in 1987 against the Pakistan Army. And in 1987-1989 the Mi-25/35s were successfully deployed against the Tamil Tigers while on Peacekeeping mission in Sri Lanka. 25 Hinds were upgraded by IAI after contract signed in 1998. The upgrade includes new mission computer, Taman night targeting system (same as on AH-1W and Israeli Cobra) with TV and FLIR sensors. NVG cockpit with MFD for the targeting. Shturm-V ATGMÂ remains its main armament, although integrated with the Taman system. India didn't order more advanced guided weapons, since the proven Shturm missile is still highly effective against older MBTs, such as the Chinese Type 59/60 still in service including Pakistan. The Indian developed Nag ATMG might be implemented in the near future. Other upgrades include GPS, helmet mounted sensor, chaff/flare and Elta warning systems.
Air-to-Air: Hind vs Cobra
I moved this topic, because I didn't think the comparison should not be based only on air-to-air combat. But I found some info. The Hind has a higher speed and rate of climb. The Cobra has better manoeuvrability, especially at low speed, which means it can out turn the Hind and make the kill. They did encounter eachother in the air defense role in East Germany. Although most often friendly flying along eachother, on one occasion it turned into disaster. The AH-1G came close to the border and the Hind was scrambled to intercept it. The Cobra followed the border by repeatedly acceleration and pitch up sharply to bleed off speed. The Hind had a tough time staying on the Cobra. And determined to stay with it this time, the Hind followed the Cobra in its pitch up, the Hind started to tumble. The pilot put the Hind into a dive to gain forward speed, but was too low and crashed, killing the crew.