Surprisingly many years ago, I faced the same choice. I shot predominantly digital and due to circumstances (theft) I was faced with the necessity to replace virtually all my kit. I shot APS-C before, but at that time, full-frame was a real contender at a comparable budget - at least for the camera. The Canon 6D was relatively new at that time, if I remember correctly.
In the end, I opted for APS-C because of overall bulk, weight and cost (also of optics). It was also very clear at that time that APS-C was a viable ecosystem with more than enough equipment for me to choose from. In the very specific choice I made, which ended up being the full-frame Canon 6D against the APS-C 7D, I also noticed that the 7D was basically a more 'mature' camera with a more pleasant viewfinder - it somehow looked bigger and brighter than the 6D's.
I know back then about larger pixels, better S/N ratios and the potential for cleaner high-ISO images from a full-frame sensor. But at the same time, the comparison only becomes concrete if two specific cameras are pitched against each other, since technologically, not all cameras are equally advanced, and one full-frame sensor may easily rely on outdated technology and offer poorer S/N performance than an APS-C sensor that happens to be more modern. 'Ceteris paribus' does not always hold true when comparing two specific items.
What to make of all of this? The choice is personal, and very much a practical one. For me, bulk and weight were decisive criteria. For someone else, compatibility with already owned optics may be more important. We all decide on different criteria. I think the main thing is to work out which criteria are relevant to you, and then decide which products suit those criteria. E.g. the high-ISO performance of modern FF cameras may be better than of equally modern APS-C cameras, but it's very well possible that both meet your needs already. It then becomes the question how much you want to shell out, and how much weight you're willing to carry, for the technically unnecessary 'excess performance' of one system vs. another.
One final thing is quite relevant. Of course, full frame holds the aces in terms of bragging rights. I think many, if not most, FF cameras were sold on that basis.