To start, I'm also not sure there's any standard terminology here. Unless there are even more models above than I'm aware of, Gledopto's RGBCCT contoller is a 6-wire module: one each (three total) for RGB, one each for warm and cool white, plus the "V+" line for power. There are some 5-wire controllers out there for RGB plus fixed white, and there are others for just RGB, CT, or fixed white. On Hubitat, the best-match driver for a 6-wire controller like this would be the "Generic Zigbee RGBW Light" driver, as Hubitat considers "RGBW" to be RGB plus color temperature (not just a fixed white; this is why you see CT commands in the driver). There is no good fit for a 5-wire controller, but RGB would be a good option for at least the color portion unless you have a "2 ID" version and the RGB and white/dimmable portion show as separate devices (the "1 ID" vs "2 ID" thing is a separate issue but the important takeaway from either is that the former will show as one RGBW device and the latter as one RGB plus a second white/CT device, depending on real device capabilities, on either Hue or Hubitat).
The same is true for Hue--it has a concept of "extended color light" (RGB + CT, or RGBW in Hubitat-driver terms--and it will get added via the integration using a driver called hueBridgeBulbRGBW). Hue also has a "color light" (RGB, like first-gen Hue Lightstrip), "color temperature light" (CT-only, like White Ambiance), and "dimmable light" (fixed white, though technically anything; a Hue White or Hue Lux are native examples). This lines up with both the Hubitat native/direct Zigbee and Hue Bridge drivers offered. But there is nothing for a "color plus fixed white"-type light. Again, Hubitat has a driver for all of these other combinations, so your experience on Hubitat vs. the Hue Bridge should match.
As for Bridge vs Hubitat: in my opinion, Hue does a better job with lights than directly-paired lights on Hubitat. It is fast, reliable, and natively supports Zigbee scenes (an on-device scene table that can be recalled on multiple lights at once with a single group broadcast; Hubitat emulates scenes with multiple commands, one to each device with the desired setting for that device--theoretically not problematic, but at the very least subject to the so-called "popcorn effect" where everything happens in quick but noticeable succession rather than all at once, to say nothing of problems some people have with directly-paired lights on Hubitat not responding to commands the first time around).
That being said, it is not my opinion that the Gledopto controller is good at all. It seems pretty slow to respond to commands in general, whether directly paired to Hubitat or used via a Hue Bridge (even when controlled directly from Hue). It's the only third-party controller I've used, so I don't have much to compare it to, but only the Ikea Trådfri bulbs have been this slow in terms of third-party Hue-compatible devices I've used, and both are a far cry from both native Hue (which I wish I would have just paid for here...) or most third-party products. Your needs or opinion may vary.