Avoid both! Both briefs and boxer-briefs trap lots of heat! They are very bad for your testicles. You do Not want both compression and over-heating. Think about it: You compress and prevent your testicles from dropping to cool--and then you also overheat them? That's a recipe for cooked balls.
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​Conclusion: Avoid supportive underwear that has poor heat ventilation. Unless you want  testicular damage.

Supporters and jockstraps are the worst! Not only do they typically trap a lot of heat, but they also typically over-compress the testicles. You really cannot find a good compression supporter because they all squish your testicles and penis together into a ball! Someone really didn't understand why your testicles are outside of your body when they designed these things.

Conclusion: Avoid both supporters and jockstraps whenever possible, unless you want impaired testosterone and fertility. 

Boxers seem like a good option at first... I mean, they are more breathable right? Well, no, boxers trap just as much heat as briefs, because they typically have much more fabric! I have yet to find any boxers that are good at ventilating heat, and believe me, I've search through dozens of brands! Moreover, boxers allow scrotal sagging--which does not look good, and is unhealthy in the long run.

Conclusion: Boxers seem like a good option at first, but they are Not. Try to avoid boxers unless you want testicular overheating and scrotal sagging (which is unhealthy in the long-run).

Going commando is probably the best option so far. I mean why are our balls--the one body part that needs to be kept cool, wrapped up in multiple layers of clothes? It's irrational--an irrational social norm. Even though going underwearless  is the best option for keeping your testicles cool, it still doesn't provide scrotal support.

Conclusion: Likely, by far the best option here--much better than briefs, supporters, and boxers. Going commando is a good option.

The best cooling underwear is one has a specially designed fabric, separates the penis and the balls, all at the same time providing light support for the testicles--improving blood circulation and not over-heating the testicles.

Conclusion: Buy the STUD Underwear it is the best cooling & testicular support underwear. It is great for varicocele.

5 Reasons to use Stud Briefs for varicocele natural treatment: Cooling, seperation, surgery-free solution, discreet varicocele treatment, and improved circulation.

Boxers provide no benefit for varicocele because they trap heat, and do not provide no support. This means both scrotal sagging (increased varicocele size) and overheating. 

Do not wear briefs if you have a varicocele. The main problem with briefs is that they squish the testicles and penis together into a ball. This traps lots of heat. Compression and with over-heating creates testicular dysfunction (it prevents the testicles from dropping to cool, and over-heats them too.)

Scrotal support underwear has the exact same problem as briefs. They compress the testicles and penis into a lump, over heating them and preventing the testicles from dropping to cool. They cause a lot of damage to the testicles. Many ill-advised doctors recommend scrotal supporters for those suffering from varicocele. 

I advise going commando over wearing boxers, briefs, or supporters. Cooling should take precedence over compression. Without cooling compression is dysfunctional. 

The best underwear for varicocele provides maximum cooling, separates the penis and testicles, and provides healthy scrotal support & compression. These combined together are very beneficial for varicocele. They help cure varicocele pain, reduce swelling, and improve both fertility & testosterone. 

When you combine compression, overheating, and varicocele, you get testicular damage. If you copress the testicles you prevent them from dropping down to cool-down when they're over-heated. From here, we know that varicocele disrupts normal testicular cooling. So, the testicles are almost always wanting to drop down to cool. But if you compress them up, they cannot even do this. Add poor heat ventilation to this, and you not only trap lots of heat, but your testicles have no way of cooling down. This means testicular damage--as in testicular shrinkage, infertility, and impaired testosterone.