I'm mixed on this.

One thing that I think is often missed is that the way subdomains are used vs subfolders.  A lot of times when you have a subfolder - it is linked within the internal structure of the site, while subdomains are not.  So link juice is not passed. That's why you don't see *.wordpress.com or *.blogger.com sites outranking everything under the sun, none of the root domain juice is passed down to the subdomain.

However, we've seen for our clients that subdomains still work as long as it's part of the internal link structure - with the added benefit of having 2-4 serp results (mostly with branding type queries).

So with that said, reverse proxies are not the necessarily the same as 301 redirects. In general, you would use a reverse proxy if you had content on a remote server and the easiest way to serve that content is using a subdomain - by using a reverse proxy you can instead use a subfolder instead.  While a 301 redirect, is generally used to redirect a page to a newer/canonical page.

However, if you're talking about the best solution to handle subdomains - 301 vs reverse proxy.  You may end up doing both if you're using a reverse proxy, you may have to 301 redirect certain content pieces... especially if you're proxy doesn't properly redirect/handle relative paths.  The issue is talked about in the comment section.

If you're starting a completely new site - my guess would be that a reverse proxy would be better than a 301.  As a reverse proxy would not lose any link juice - in theory.

I'm mixed on this.

One thing that I think is often missed is that the way subdomains are used vs subfolders.  A lot of times when you have a subfolder - it is linked within the internal structure of the site, while subdomains are not.  So link juice is not passed. That's why you don't see *.wordpress.com or *.blogger.com sites outranking everything under the sun, none of the root domain juice is passed down to the subdomain.

However, we've seen for our clients that subdomains still work as long as it's part of the internal link structure - with the added benefit of having 2-4 serp results (mostly with branding type queries).

So with that said, reverse proxies are not the necessarily the same as 301 redirects. In general, you would use a reverse proxy if you had content on a remote server and the easiest way to serve that content is using a subdomain - by using a reverse proxy you can instead use a subfolder instead.  While a 301 redirect, is generally used to redirect a page to a newer/canonical page.

However, if you're talking about the best solution to handle subdomains - 301 vs reverse proxy.  You may end up doing both if you're using a reverse proxy, you may have to 301 redirect certain content pieces... especially if you're proxy doesn't properly redirect/handle relative paths.  The issue is talked about in the comment section.

If you're starting a completely new site - my guess would be that a reverse proxy would be better than a 301.  As a reverse proxy would not lose any link juice - in theory.