I have only built one 1911, and I did it buying a bare armscor frame and a parts kit from sarco, and then replacing most of the internal parts with Ed brown parts. I hand fit everything, ground the frame to a radius for a beavertail grip safety etc., made my own rosewood grips and then completely finished it.
My experience on that, is that there is a lot of variation in parts. I actually couldn't make the thumb safety that came in the parts kit function. Using the kunhausen manual, I determined that pretty much all of the parts were in spec, but when you have one part that is at the max dimension and a couple other parts that are at the minimum dimension, it still doesn't work. You will have this anytime you buy a mixed bag of parts, but the better quality parts you go with the less likely you are to have problems, or at least the more you stick with one brand the more consistent they will be on tolerances.
You also have a certain level of doubt in your head as to the quality of parts you are using when you start with the bottom end, and that can mess with your head while you are fitting things. It gets very easy to blame this part or that part because of the price, rather than to actually trouble shoot and make it work. When you are working with an Ed Brown, or Wilson Combat quality level part, you tend to assume it is right and not just jump to conclusions that you need to swap things. Since I basically started with an RIA frame, I would surmise that my experience would hold true for buying an RIA pistol to base your build off of. It will work, but you will find yourself doubting things as problems arise and the "good parts" don't go right together with your "cheap parts". I think paying the extra up front for a fusion or caspian kit will give you more confidence as the project goes, but won't necessarily make you a better gun in the end.
The other advantage I see to buying a dedicated build frame/slide is you can generally get them in the finish (or lack thereof) of your choosing. The frame I bought did not match the finish of the slide I bought, and both required refinishing anyhow, after all modification and fitting was complete. Cleaning the parkerizing or whatever it was off of the frame was a pain, and also required me to remove material (a very small amount, but still). While I didn't take material off any critical areas, you can't really put it back. Starting with a bare metal frame, gives you a lot more options.
If this is your first build,than I would recommend going the RIA route. Start with a gun that works, and try to make it better. Starting off with a ziplock bag of parts and not knowing which ones were good or bad, made my first build a bit of a challenge. Change one part at a time and see where you end up.
If you are an experienced builder and are starting off with a vision of a particular gun in mind, then going with a caspian frame, or a fusion kit may be a better choice for you as you won't spend time trying to undo anything like parkerized finish, or over buffed edges you may find on a factory gun.