LS3/5A vs Tannoy

For Tannoy, I mean Tannoy co-axial speakers such as monitors and little gold (not giant PRESTIGE cabinets).

both are British. Which one is better? Which one is more musical? Which is better for classical music?

Both are exceptionally good in all facets, but require quality electronics and cables to make them shine. For example, don't try to marry them up to a receiver, but instead invest in quality British source and amp.

Without knowing the rest of your system, any recommendations are regrettably nothing more than heavily biased value judgements with nil assurance that they will work in your system ( ... ergo ... useless opinions)
If you are a dynamics or led zeppelin kind of guy the LS35a's might not quite do it for you. On the other hand they excel at things like jazz and pop vocals, violin concertos, string quartets.
Back in the late 70's I had the 15 ohm Rogers LS3/5a, with Dynaco tubes and solid state from Yamaha and Nad 3020.
The sound was very nice and very polite in the small room they were in.Later they fell apart when placed in a larger room.
The detail and image of the Rogers was very good, but it was always like a very nice miniature of the real thing.

Thrty plus years later I had Tannoy Ardens and again tubes this time a Cary 300B, then solid state Red Dragon monos.
Both made the Tanoys sing in a large room, but not the same home as the Rogers were in.This room is twice as large again.
I also had on hand a pair of Bobby Palkovich's scary mini monitors,and to my ears they had a lot more detail than the Tanoys. but lacked the bloom of those big English beasts.

So it's about trade offs.
At least that's been my experience with the speakers and systems I've mentioned.

The best advice I could give is that you try to audition whatever speakers you are interested in your room and with your gear.
One size does not fit all.

And one other thing to keep in mind, what impresses you today, or this week or next month, may not in the not too distant future.

I have friend who changes speakers as often as he changes his shirts, and he still hasn't found the "right ones" yet.