They're quite different despite both being oolongs. Tie Guan Yin (TGY): Lightly oxidized (10-20%), rolled into tight balls. Flavor is floral, orchid-like, creamy, green. Lighter feel. Very popular, easy to find decent quality at your budget. Da Hong Pao (DHP): Medium-heavy oxidized (40-70%), often charcoal-roasted. Flavor is mineral, roasted, complex, woody, sometimes chocolatey. More body. The famous original bushes are ridiculously rare/expensive — anything at $20-30 is 'Wuyi rock oolong' blend which is still good.
For ease of brewing, TGY is more forgiving. You can brew it at 90-95°C, 20-30 seconds, and it's hard to make it bad. DHP needs more care — overbrew it and the roast becomes dominant and harsh. For first purchase I'd say TGY gives a clearer example of 'Chinese oolong' as a category. DHP can follow.
At the $20-30 range you'll find both. Look for traditionally roasted TGY (碳焙) for a middle ground — it has the floral TGY character plus some roasted warmth. Very accessible.
Bought traditionally roasted TGY based on PuerHead's suggestion. It's incredible. The floral-roasted combo is exactly what I was looking for. DHP is on my list next.
