'Full Frame' bodies really have only a few advantages over 'APS-C' bodies, and they're not that significant. There is a lot of myth, lore and misinformation on the subject, and I find it frustrating that so much of it persists. This is my attempt to clear up some of it.
A larger image sensor provides a more shallow Depth of Field for images with the same perspective. For instance, a 'Full Frame' body with a 105mm lens and an 'APS-C' body with a 70mm lens, will produce almost identical images with almost identical perspectives. But with an aperture of f/2.8 and a subject distance of 10 feet, the 'Full Frame' body will get a total DoF of 0.45 feet while the 'APS-C' body will get a total DoF of 0.69 feet, which is about what the 'Full Frame' body would get with an aperture of f/4.0. If the 'Full Frame' body was using a 24-70/2.8 lens and the 'APS-C' body was using a 17-50/2.8 lens, they would both be capable of almost identical images, but with an aperture of f/2.8 and a subject distance of 7 feet, the 'Full Frame' body would have a DoF of 0.5 feet and the 'APS-C' body would have a DoF of 0.66 feet, about what the 'Full Frame' body would get with an aperture of f/4.0. And if the 'Full Frame' body was using a 70-300 lens and the 'APS-C' body was using a 55-200 lens, they could both produce nearly identical images, but at f/5.6 and a subject distance of 100 feet, the 'Full Frame' body produces a DoF of 11.4 feet, while the 'APS-C' body produces a DoF of 17.3 feet, about what the 'Full Frame' body would get using an aperture of f/8.0. So the difference in Depth of Field is only about a single stop.
A larger sensor performs better than a smaller one, but few attempts have been made to quantify the difference. DxOMark.com performs a series of measurements on many cameras, and publishes the results on its website in such a way that the results from different cameras can be compared. It publishes a lot of "scores" and other values that seem to be actual measurements, but the only two that are direct measurements are for SNR 18% (signal to noise ratio) and Dynamic Range (the luminance range, from brightest to dimmest.)
The results show that, for instance, the level of image noise of Canon's 'APS-C' 7D Mk II is 35.5 dB at an ISO setting of 400, while the 'Full Frame' 6D scores 36.2 dB at ISO 800 and 33.4 dB at ISO 1600. That works out to the 'Full Frame' 6D having about a 1-1/3 stop advantage over the 7D Mk II with respect to noise. Similarly, the dynamic range of the 7D Mk II at ISO 400 is 11.39 Ev, while the 6D scores 11.55 Ev at ISO 800 and 11.12 Ev at ISO 1600, giving a 1-1/2 stop advantage over the 7D Mk II . (See Canon EOS 7D Mark II versus Canon EOS 6D)
Nikon's 'APS-C' D7200 scores a SNR 18% of 33.7 dB and a dynamic range of 11.89 Ev at ISO 800, which gives Nikon's 'Full Frame' D610 a little over a one stop advantage in noise and about 1/3 stop advantage in dynamic range. (See Nikon D7200 versus Nikon D610) In addition, Sony's 'APS-C' A77 Mk II scores 35.6 dB and 11.52 Ev at ISO 400, roughly 1 stop behind Sony's 'Full Frame' A99, in both measurements. (See Sony SLT Alpha 77 II versus Sony SLT Alpha 99) So there is certainly a promise of improved image quality with larger image sensors.
One of the advantages of 'APS-C' bodies over 'Full Frame' bodies, though, is the abundance of lenses, both 'Full Frame' and 'APS-C only' ('EF-S', 'DX', 'DT', 'DA', 'DC', 'Di-II'), and one of the disadvantages 'Full Frame' bodies have, when compared to 'APS-C' bodies, is that many 'Full Frame' lenses exhibit additional vignetting, distortion, transverse chromatic aberration and/or field curvature that don't appear when those same lenses are mounted on 'APS-C' bodies.
So while a 'Full Frame' body may be capable of better image quality, the lenses may have trouble delivering it.
It's your call, of course, but the advantages are not nearly as great as I've heard some say, and I think you should know exactly what you'd be getting yourself into. If you need the slightly more shallow DoF, the slightly lower noise, and/or the slightly greater dynamic range, and you can find an appropriate lens or lenses from the limited selection, to give you the results you want, I hope it works out well for you.
But there's very little you can't do with a smaller, lighter, cheaper 'APS-C' kit.