Which one is better for online gaming, ADSL or DSL?

You do know that DSL stands for
Sigital
Slow
Line
right?

So, neither would be good.

DSL is not a good line to use. You need cable to fiber optic if you can afford it. Most online games these days benefit from the fastest connection you can use. I used to use my DSL about 12 years ago when I had my Dreamcast.

Depends. ADSL is rather poor. DSL such as VDSL2 can be fine. But those are usually only available when the DSLAM is near such as in same apartment building.

FYI: ADSL or Asymmetric Digital subscriber line is sub set of DSL or Digital subscriber line...

ADSL is a subset of DSL. If the choice is between symmetric or asymmetric, his choice is between a form of ADSL and a form of SDSL. SDSL gives more or less equal upstream and downstream speeds (the allocation can change depending on various things), ADSL trades upload speed for more downstream speed so they are imbalanced by technical design. And it depends exactly what types of ADSL (ADSL2+?) and SDSL (VDSL?) we're comparing. And a number of factors drive what speed your friend will actually get.
Now all things being equal, if ADSL gave 24Mbps and SDSL also gave 24Mbps, I'd go with SDSL since it meant the upstream would also be 24Mbps whereas the ADSL upstream would be like 3Mbps (keep in mind those are technological maximum speeds which will never be reached in reality).

The other thing though is that multiplayer games generally don't need more than 1Mbps up/down, latency (ping) is the bigger concern. If the choice is between say, ADSL2+ @24Mbps down/3Mbps up, and VDSL2-plus @300Mbps down, but the difference in latency means ADSL+ gives a 15ms ping while VDSL2-plus gives a 30 ping, technically ADSL would be the better choice for gaming if nothing else were considered. But depending on the price difference that trade off may not be worth it. Often VDSL can give higher latency by design.

TL;DR is, there isn't a definite right answer. Symmetric is probably better bandwidth, but it won't make much difference if you're getting 1Mbps up and down. Latency is more important. In reality you want to consider factors such as the price difference, how else you're using the internet besides gaming, and the actual speeds your friend will achieve at his residence versus what the theoretical maximums are (which he may not know until he's connected).

Believe It or not we still had coaxial cable for internet and phone a month ago (ADSL probably). And the latency was ok for 2 years. Then the company bought another one and everything went to hell. "Resistence" or "saturation" they call It.
Coaxial is susceptible to noise but I think your friend could ask them for a better type of. Hope he gets good numbers.