300B SET or EL34 SET

You have got some great answers but not all that I would completely agree with.  If you really love your 89bd speakers then you have to find the right amp for the job.  Ralph is 100% right a 300b amp needs 103 - 104 db sensitive speaker to really perform.  In a smaller room also.  So if you are going to keep your Tannoys match it with a much more powerful amp.

EL34 is not good, IMO, idea for audiophill listening, it is more for guitar amps with more sharp sound, that people senses like detail. I had SE EL34 and SE 300B, and 300 B is better variant with more wide scene. 
If You use instead SE output transformer PP transf. with one shoulder for 300B sounding and second shoulder for compensating idle current, bass will be max! Saturation, that is main enemy for sounding and bass,... will be zero! Now I have the same construction with EL11 Telefunken and sound is amazing with small PP transformer.

.....Construction SE /pseudo PP/ is my work.

Maybe I have to look at another Tannoy speaker which is more sensitive. I suppose the bigger brother Cheviot (at 91dB) will sound very much like my Eatons. Then there are the Prestige series Turnberry GR (at 93dB), but I have not found anyone who have compared Turnberry with Eaton or Cheviot, so I don't if they have the same "house sound".

Or maybe I, as bobheinatz says, use a more powerful amp. I already have an old Tube Technology Unisis Signature (that needs a little repairing), EL84, PP, 30-35w and a Line Magnetic LM34IA, EL34, PP, 40w. These are the amps a use whith my Tannoys today.

I should never had heard these Audion amps:)

@azazello
I have a PP EL34 amp today and as I said before I really like the EL34 tube and I can't agree with you that it's not a good tube. Maybe it's a question of taste or maybe it's a question of room, DAC, other components in the amp or...

Plga just curious which class d amp is blown away by the LM tube amp?  My experience has been less than positive with class d.  Even super quality high priced class d amps like SPEC tend to get less play time in my setup. 
Mastersound makes a nice el34 that can be played in triode or UL.  You may also like the Leben sound but you will pay for one because there is a lack of distribution or production.