I own both a gaming PC and the Switch so I'll give you my 2 cent.
I'd go with the gaming PC. There are many reasons and I'll try to list them.
Reasons to go with the PC:
1. You can do more than gaming with the PC.
2. Games (especially older) are significantly cheaper. I've been paying $80 (CAD) per title on the Switch vs $40-50 for PC. Even new release titles are about that much if you want to hunt for deals. (Recently bought Forza Horizon 3 for $50 and Dirt 4 for $40)
3. You are not locked to a controller. You have the option of mouse + keyboard or a cheap $20 xbox 360 controllers. Splatoon 2 on controller was extremely difficult.
4. Although Zelda + Mario Kart + Odyssey are really good, some of the best games ever made can be found on PC. Skyrim, Witcher 3, HL2, all Blizzard games, etc.
5. Esports titles like PUBG, Overwatch, LoL, Dota, will never exist properly on consoles. Yes PUBG is coming to Xbox, but all tournament plays will be PC and always PC.
6. MMORPGs will probably never exist (properly) on consoles, unless it's like a 2D Pokemon MMO game. (plz Nintendo)
7. More games are available for PC, and always ever will be
8. Never Obsolete! Look at the Wii U. After the Switch release, the Wii U is pretty much obsolete, This will happen to the Switch years from now. PC will be upgradable and when it becomes "obsolete", you can use it as a secondary PC for just browser/file manage/TV PC or give to a family member.
9. Switch has expensive accessories. I had to pay $100 (CAD) for a second pair of Joycon + $30 for a Joycon charging kit + $15 for the Joycon grip. I will likely also buy a third-party mobile dock later on which will be another $60.
Reasons to go with the Switch:
1. Portability. If you want to play on the go, it's not even a question. Buy the switch.
2. You really want to play first party Nintendo games like BoTW, Odyssey, or Mario Kart.
3. If you don't need accessories for the Switch, the physical game console will be cheaper than PC overall. With PC, you will need to consider things like gaming mouse/kb, headset, and upgrades later on like SSDs, RGB!!!, monitor, webcam, etc. But generally the PC accessories will be offset later-on by the lower cost of games.
4. Buy physical copies to resell/trade. This can offset some of the cost of the game.
5. Don't want to sound crude, but a PC for about $400 is gonna be kinda crappy. You may not have the best experience with it. Console will be a better experience since gaming is the only thing it can do.