I also have done both, and prefer the stand-alone for recording and a PC for editing and mixing.
We have had some success with recording with an interface and a PC, but we have had a lot of headache with latency and pops, clicks, and dropouts, due to buffer size or software settings. Sometimes we fight a weird delay that is simply nausea inducing, making simultaneous playback/recording really hard.
But editing on a PC is easy and works well.
Recording on a stand alone unit has never given me any latency, delay, pops, clicks, or weirdness. I don't have to figure out software settings. I don't search the Internet for drivers or fixes. I never catch the singer running Facebook in a background window, or have problems with resource sucking stupid programs doing unwanted things in the background. The stand alone units are purpose built for one function, and they do it pretty well: harvesting tracks.
But the ones I have used can be difficult to edit, mix, or add effects.
Much of this may be driven by the fact that I am a cheap scumbag and I am not using top-of-the-line gear. Any PC I use will be multi purpose, an somebody will be browsing Facebook, and the kids will be playing games, and somebody will always be accidentally downloading sneaky crap software that continually runs when nobody consciously ask for it.
I imagine that if you have enough money, good computer skills, and nobody else mucking with the computer while you are at work, the interface and PC route works excellent. It mostly causes headaches for a common dufus like me.
Stand alones go pretty cheaply used. Often as cheap as (or cheaper than) a good interface. If you can go with only grabbing two tracks at a time. Stuff like a Tascam DP-02 is $150 or so. Audacity is free. Reaper is $60. You may already have a crappy PC. How expensive is a GOOD interface and a GOOD PC?