Your NAD T753v3 is not Class D, while the T778 is Class D. I have both an NAD 275BEE (Class A/B) and the newer Class D amplifier, NAD C298.
The increased power of the Class D amps are notable. While class D is still "musical" as I have found all NAD amps to be, it is a different animal that certainly changes the sound signature - especially if driving speakers that are power hungry.
For example, the NAD C298 sounds much better driving my Wharfedale Heritage Linton speakers, that go down below 4 ohms. Transients are faster and the C298 is more revealing. However, the NAD 275BEE is more "expressive" (as a lower watt tube amp could be characterized) with a pair of ML 35XTi’s I have with AMT tweeters. To some extent, the power of the c298 can overwhelm a bookshelf speaker like the ML 35XTi, or perhaps any speaker that only dips down to 6 ohms.
My point is that not knowing what speakers you are using makes it hard to convey what kind of power you need, but if you have 4 ohm speakers, a class D amp will certainly make a difference in sound signature.
Also, the fact that the C298 emits zero heat is important since my amps sit near my listening seat and the 275BEE does get moderately warm after a few hours of play. Kinda a big deal in my basement that has no HVAC assistance.
The touch screen provided by the T778 may not even be something you use if you can use a remote app as effectively. Screens add fair hardware costs but do nothing for sound. Which is what you get with HT amps, a lot of features that do not correlate to better sound.
You may want to consider the NAD M23 as it is a class D amp and about the same price as the "feature rich", NAD T778. If you have a stellar set of front speakers that you use for 2-channel stereo, then there will be a fair difference in sound when you compare the T778 sound vs. the M23 - especially if those speakers dip down to 4 ohms or lower.
Your NAD T753v3 has been discontinued in favor of the T753v3i. No real viable difference in the models. That means you can still get a good price for it. Once the v3i is discontinued, expect to lose up to 30% of resale value or more. I have always tried to rid myself of something before it loses it’s luster on the open market. It’s the reason I still have the ML Motion 35XTi’s. When ML came out with the B100 - which is pretty much the same thing without the wave guide - my 35XTi’s became a hard sell. Most recently, the Music Room offered me $350 for both of them, which was kind of insulting, since I paid $1,500 for them just three years ago. I simply waited too long to make the change. You may want to see what you can get out of your T753v3 (Music Room is a good start) before you take the plunge on a replacement.