I'm looking to get a new PC for my Sonar X3 and want to separate my audio and maybe projects from the rest of the computer for improved speed. Would love opinions on whether to install a second hard drive or use an external USB 3.0 drive. I would think internal drive would be much faster but appreciate any suggestions.

I would definitely go with an internal HDD for audio and projects, make sure it's 7200 rpm spec.
The external USB3 drive would be great for off computer back-ups.

I haven't tried USB 3.0 but I imagine that an internal SATA will be faster, and frankly I wouldn't want any potential bottleneck between my audio files and my memory.
 
My desktop tower has 4 drives: 2 SSD and 2 rotating iron for backups. I also backup to external USB 3 drives but they aren't the primary storage.

Hi. I agree with the advice given so far. Go for an internal HD / SSD.
I've got 4 SSD's in my studio pc, and back up to external HD's.
All the best.

Standard drive config is...
Drive 1: OS, Software, Plug-ins
Drive 2: Project and audio files. These don't need to be separate. As a matter of fact, your audio files will be located in each of your separate project folders.
Drive 3: If you have any streaming sample libraries (like many of the ones made for Kontakt), a third drive can improve performance.
 
Configurations can vary of course. Some people like to keep the OS and software on separate drives, etc. That's up to you. Also, another external drive for backup is a very good idea.
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Yes to both.  Good idea to put your projects and audio on 2nd drive.  Get the USB for backups.
 
Most modern motherboards have at least 4 SATA connectors so you can connect up to 4 SSD/HDD drives.

 I have a  128 GB SSD  C drive,  a 240 GB SSD (F) is my working Sonar drive where most of my projects and Wave masters are kept,  My 3rd dive is a 1 TB 7200 (G) drive  with back ups and sample libraries. Once an album project is finished I move it to the G drive as well as everything is also backed up externally and on 2 other computers so 4-5 backups for most projects. 
The price of SSD drives has come down on the bigger drives so if I was  re building right now both my C and F drives would be bigger. External drives are also dirt cheap and I just bought a 2 TB for under $100 I'm going to load up and take to work as an off site back up. 

Internal drive, 7200rpm HDD or an SSD. Either is faster than any variety of USB connected drive. A USB3 5,400rpm USB-powered external drive can stream stereo audio or 1080p HD video easily, but multi-track audio where you want it to be reading and writing completely glitch-free at the same time is a different matter.

USB 3 external drives are good for making fast backups though.

Yes, this is the most important spec (7200rpm).

An USB 3 SSD is actually really fast. I'm surprised, it sounds as if nobody here tried it? Up until recently all the above was true but a USB3 SSD is faster than an internal 7200rpm traditional HDD and only marginally slower than an internal SSD (unless you're talking M2/PCIe).

While I personally prefer to keep things internal (and it IS a little bit faster, given you'd use an SSD for either situation), I can definitely understand the convenience of a USB3 option if you're planning to move projects between a laptop and a desktop.

Unless you're talking ultra high track counts in your projects or intense sample streaming, I doubt you'd ever notice the difference between a USB3 SSD and an internal one.