Like others here, I built my own rig.  
 
I went to Micro Center and bought all my parts even the case, which is padded inside.  I  picked out the MOBO I wanted, got the 32 GB.'s of Ram I wanted, selected 6 the internal fans I wanted with automatic temp sensing and adjusting. I selected my i5 4th Gen Haswell Processor, I chose my own GeForce Video Card with Direct Direct X 12 and my own cooling system. I selected my own two internal DVD writers and finally, I based my power supply on how much power my PC will need, not what a PC manufacture wants to give me. then I install it and was happy with the outcome.
 
So, that is why I build my own PC, because I know what's in my Baby and I can change anything I want at any time!

Like the others, I've always used desktops that I've built myself from parts. More umph for the money and more flexibility to upgrade over time. Current system is an i7 chip, SSD for the OS, SSD for plugs and sample librarys, Spinning drive for audio, 32gb RAM. The machine is built in a 2-space rack mount server case and drives three monitors without breaking a sweat.
 
The power supply isn't fanless, but the fan is super quiet most of the time. Same with the chip fan and case fan. The system is super quiet. I can easily record audio through condenser mics with no detectable fan/computer noise in the track.

Jesse G
Like others here, I built my own rig.  
 
I went to Micro Center and bought all my parts even the case,

 
so did I.
you use the one here in Cambridge Jesse ?
(im from right here in Boston = a suburb outside of bean town)

I run an old Intel i7-2600 with 24GB Corsair RAM, 650W silent PSU and 3 x Seagate 2TB drives. Coolermaster Silencio case. The machine works 10+hours per day, 6 or 7 days per week and has been for about 6 years.

It may not sound impressive, but it is the heart of my studio and the tool I pay my way with. If anything goes wrong with the OS (Win 10 x64), I can grab a cloned drive from the safe, rip open the side and be back in business inside 10 minutes - before my clients have finished their coffee :O)
It recently got its first PSU replacement because the old one got noisy. That took 30 minutes to replace and just a few bucks.
 
I don't think you can say the same about the average laptop, neither about speed of repairs or longevity (I'm guessing).
 
Anyhoo, that's my workhorse..

chuckebaby

Jesse G
Like others here, I built my own rig.  
 
I went to Micro Center and bought all my parts even the case,

 
so did I.
you use the one here in Cambridge Jesse ?
(im from right here in Boston = a suburb outside of bean town)

Same here except from the one in Dallas.
 
Desktop here. As a bit of an equipment freak, the desktop allows much more external connections than a laptop. The only things I 'require' for my desktops are intel processors, Western Digital HDD's and Nvidia graphic cards. These are personal preferences but I won't stay home without them. :) I would also spec an intel motherboard but they quit making them. (sigh)

Self built desktop (with the help of Jim @ studiocat, he's a really cool guy).

Desktop.  Monster desktop.  In thirty years of scratch-building ever-smaller PCs and servers (most of them rackmounts), I've also taken a tip from the gaming community and returned to the world of honkin' big towers.
 
Re AMD vs. Intel, my experience mirrors your own.  My last audio workstation was a scratch-built AMD and unreliable as hell.  Random BSODs and system lockups were so predictable, in fact, - once every two or three days - I had Sonar doing automatic saves every five minutes.
 
My latest machine is a scratch-built Intel i7 with dual SSDs in a RAID 1 configuration.  [Can you tell I have zero tolerance for failure anymore?]  The hardest part of this build was finding a motherboard that supports legacy PCI for my Lynx AES16 digital audio card.  Thankfully, there's still a few motherboard manufacturers making new products with PCI slots, and I've been very pleased with this Asus P9X79 LE.  I hate to jinx it, but even on Windows 10, this is proving to be my most reliable audio workstation yet.
 
If you're interested, I composed a blog article and time-lapse video of the build, complete with parts list:  Scratch Building the Audio Workstation of Penultimate Doom.  These things get dated pretty quickly, but maybe it can help?
 
Good luck!
 

Self built Desktop for sure.  Nothing wrong with laptops, but I like that I can configure my desktop any way I want.
Built mine about 3 years ago and haven't had a problem since. 
It's the 3rd one I've built in the last 12 years (first desktop was bought from a custom computer builder/shop).
All except the custom build were solid.  Next one will be self built as well.

Eleven year-old HP Windows Media Center computer with 2048 MB (!) of RAM, with an original Focusrite Saffire. And XP.
It's okay; I'm using 12 year-old software.

Same here as most,  with main DAW my own build and a laptop for the occasional live recording. I also use various Laptops for live playback at my solo and duo gigs. I have one just for lyrics now. I hate laptops! 
I rarely have had to spend time trouble shooting desktops. And it's always simple to upgrade and fix any issues that do come up. And who could live without 2 or 3   28" screens!  
I'm fighting with my friends son's 2 year old HP laptop and a Brand new Lenovo we bought for work right now. 
I ready to toss them both out the window. The HP wireless would not connect. after 2 days I gave up and did the re install from the back up drive. That fixed it. But Windows 7 is marginally supported and you just try and run windows updates!! The Lenovo's DVD drive is not recognized anymore after out wonderful W10 nuked it. Lenovo support only says  to return it to them... at my cost 1 way! A dvd drive is less than the shipping but that voids the useless warranty. So please don't rave about laptops around me right now.. Buy an iPad and get real...,,Oh ya, can't run Sonar yet.. but it's coming..