What could be the differences between the Spendor A4 and A7 in terms of sound quality?

Personally I think you neither want nor need grilles for the A series. Though it is chintzy not to include them.

Room size may dictate your choice as well in terms of how much bass, and thus speaker, is appropriate.

the A7's, in my 13 x 23 room, produce superb bass at times and are pretty easy to position. I have the front baffle about 26" out, positioned along the long wall. I actually seek out music with lots of upright bass now. Not as chest thumping as some other speakers but they dig deep and very articulately. Almost like a larger sealed box.

I don't think the A4 can go there with the simpler bass port, D7's have even better bass of course but may need to be further out as per @kren0006 above, again depending upon room.

As a recent A7 owner and exhaustive researcher, I will throw in my 3 cents for both the OP and @glow_worm:

1. I have not heard the A4's but I am not aware of anyone who does not think that the A7 sounds better than the A4. The bass port, larger cabinet, and dampening are the main reasons. That’s an easy binary if cost is not a big issue.

2. D7(.2) is definitely a step up technically. But some don’t like the analytical top end. I am personally tempted to try the D7.2 but early reviews suggest it’s not much different. Even leaner if anything.

3. Tubes go very well with modern Spendors. I am using a 48wpc Line Magnetic LM-805ia and the synergy is amazing. Note that the smaller A4 is less sensitive and on the flip side, while the D7 is a bit more sensitive it has a lower impedance and thus a bit harder to drive.

So if you are concerned about the PL 34 watts the A7’s may be the safest match. That said, tubes might also mitigate the extra sparkle on the D7’s and bring it to perfection. I know there are others who happily run tubes with the D7’s.