I considered BCS myself instead of discrete PIDs so I'll give some ideas from the thought process I went throug a few years ago.
My goals may be different from everyone else so it's important to weigh your own goals against both methods and decide for yourself. There's really no right or wrong answer here.
Industrialized: One of my design goals was to try and build a setup that was as industrial as possible (ie: you should be able to use it on a plant floor in wash down conditions. At least NEMA 12 if not NEMA 4). I didn't want to have to be careful with it. I didn't want to have to treat it like a "normal" PC and keep it in the opposite corner and wipe down my hands before using it. If I couldn't use it with wet hands, gloved hands, hands covered in sticky grist I didn't want it. (That said, I rarely get dirty when brewing but my hands are often wet). This is possible with both BCS and PIDs. Going BCS would have meant using an industrial ruggedized PC touchscreen or similar (I've designed around these in some of the plant floor systems I built years ago and see the abuse they get). So certainly possible with BCS. The only issue is cost. A proper ruggedized touch screen PC (or screen with the PC in a rugged enclosure) isn't cheap. On the flip side PIDs/switches/lights are easy to get in industrial/water resistant form for cheap.
Interface: I loved the open ended customization available with BCS. You can do anything you want. However the more I designed my brew process (make sure you do this first and have that down pat before deciding *how* to implement the process), the more I realized that the controls and custom user interface I'd be creating would be starting to mimic "old fashioned" dials/displays/controls. BCS is infinitely more flexible but I didn't find that in my case I really needed more than what I could get with PIDs/controls/lights.
Ergonomics: Using a physical switch or button with tactile feedback is always easier for an operator than a touchscreen where the only feedback is visual. So when I design user interfaces, if I can do it with something physical I do that first if possible. If there's too much variety between screens or functions then you have to go touchscreen (I do this with my home theater remote for example). You can mix the two as well sometimes: Use the screen for display only (not a touchscreen) and still use discrete buttons. I've done that in the past with systems where an operator needs to poke at a button every minute. You don't want them doing that to a touchscreen. Give them a physical button. This was an option I considered with BCS. Just use it for display.
Flexibility: BCS wins hands down. If you're not sure of your brewing process or think you may want to experiment and/or change it in the future, BCS lets you add or remove controls easily if you keep it all on the screen. If you design correctly from the start then I really don't think it matters. I've been using my PID based setup for almost 3 years now and if I had to built it over again I'd do it the same way. Brewing's been around for thousands of years. I doubt that in 10 years we'll be doing anything radically different in our process that would make me want to redesign my control panel.
Long term serviceability: I wanted my setup to last me for the rest of my life. (I'm more interested in the craft/art of brewing than tinkering with equipment). I figured I'd spend a year or so designing something that could pretty much brew anything and then just use it forever. So part of my requirement was to make sure that if in 1-2 years (or even 10-20 years) I needed to replace something that it be easy to do. Things like relays, PIDs, switches, etc. are all extremely common parts. They've existed for dozens of years and they will continue to exist because of the tens of thousands of installations around the world running today that rely on them. I'm not married to one particular part or manufacturer. If (for example) a PID dies in 20 years I can pretty much buy a PID from any manufacturer and drop it in as the functionality will be the same. The hole sizes are all standard understood manufacturing sizes (1/16 DIN for PIDs, 23mm for switches/lights, etc). BCS is a custom controller that (AFAIK) is not open source and is owned/run by one person. Support is fantastic, Adam is a great guy, but at the end of the day anything could happen. That gave me pause. If the hardware and software was 100% open source then that may be different, but even open source stuff comes and goes in terms of popularity. Where is BCS going to be in 20 years?
Data logging: The anal retentive in me loves the idea of logging temp graphs and all those things that BCS lets you do easily and basically for "free". (No easy way to do this with PIDs). You can track all sorts of things over time. But then I started thinking: What exactly would I "do" with this data? I know how fast a PID based setup ramps. Just use the timer once to time how long it takes to ramp up. Why do I need to know exactly how that curve looks? Does seeing the curve of temp over time really give me any more information that I can use instead of just knowing the start/end points and time? Whenever people talk about all the logging they can do I always ask "So how are you using that data to make your next brew day better?". I couldn't think of one example of how I'd use this extra data so I decided data logging doesn't help me. Your needs may be different however.
Level of automation: This one's a no brainer. If you want or think one day you want to go for semi or complete automation, BCS is the way to go. PID won't give you this. BCS can replace more than just PIDs and can do all the other things you'd want for full automation like pumps/valves/float switches/etc. I didn't want semi or full automation myself so going PID was still in the running. The level of automation is one thing that I didn't actually think about very long at all. I knew right from the start that I didn't want semi or complete automation. I wanted to keep things 'simple' with what can best be described as manual dials and controls for 2 reasons: (1) So that I feel like I'm doing something on brew day (it's a hobby and we want to be part of the process steps instead of having a computer manage them). (2) I felt that the time required to program the automated steps at the start of the brew day could or would likely take just as long as 'manually' changing certain settings when needed. For example, with today's highly modified malts, I mostly do single infusion mashes (not step mashes). The only step I have is to mashout. To do that I hit the "up" button a few times. That's it. BCS could easily automate this but what exactly is that saving?
Remote monitoring/internet support: One feature that BCS is known for is that you can view your BCS controls/screen from anywhere using a web browser. Maybe it's just me, but to this day I still don't understand why I'd want to do that on a properly designed and implemented system. I know how my system behaves so I have no need to monitor it. I have timers with alarms to let me know when something needs to be done. If there's a fear that the system isn't going to run right or needs to be constantly monitored from anywhere then it probably isn't designed right to begin with. Implementing BCS controls as a web server over port 80 like this makes perfect sense of course (you get this feature for 'free'). I just think this is one of those "cool" features that is neat the first time you see it but adds little value at the end of the day.
'Bling' factor: This can most certainly be a design goal. Nothing wrong with that. If someone wants to go for the 'wow' factor then I think both a BCS based setup and manual dial/switch/PID setup can be made to look pretty impressive. A BCS setup can likely be made to look more modern with on screen dials, controls, and process pictures (even animated). A PID based setup can be made to look more industrial/ruggedized with rows and rows of physical dials/lights/switches. Almost 'retro' in a sense. Depends what style you like.
Complexity to implement: Because of the flexibility, BCS has a greater learning curve and you probably need to know a bit more about low voltage electronics if you want to fully harness the power of what it can do. Neither of these was a factor for me (I'm comfortable in this stuff). The same may not be true for others.
Long story short: at the end of day I didn't see how BCS would add any value for *my* design goals and it actually impeded some of *my* goals. I'd end up with something that behaved similarly, would have cost a bit more, and may not have been as serviceable in the long run. The key word here of course is *my*. Set your own goals and decide.