The Triaxis is going to give you a different flavor than either the Recto or the Electradyne.
It's really just a whole different set of choices.
The Triaxis tone is rooted in Mark circuit architecture for the most part.
However some versions of the Triaxis did come with the Vintage high gain recto board which is based on the orange channel of the recto, Its really kind of a different sound than a true recto but it's still a cool option to have, but if you want it to sound dead nuts recto your just going to need a real recto. There are different versions that were made over the years.
Use the search function on the boogie board searching the rack pieces section with" Triaxis versions serial numbers" and you can get up to speed on all that.
With or without it's still cool, I would just get one with the 2.0 software.
OK so just what do you get with the Triaxis?
You get a midi controllable preamp with 8 Modes "circuits" in one rack space and you can dial and assign those preamps anyway you like within the confines of the Triaixs design. The push pull options found on mark amps like shift, deep ,bright are essentially fixed in each of the Triaixs modes which can be a bone of contention among some folks. The Five band EQ also is basically reduced to a number value where you can increase the scoop with one number and increase the depth of it's mix with another number value. The EQ can however have a different setting for each preset. It's basically a compromise to get all this stuff to fit under the hood of a 1U rack space. It's not perfect in this regard but it's still cool.
Regardless you can take just one of those modes and dial it up ten different ways and assign it to one bank of your midi controller, or you could could use eight different modes and dial each one up and store that to your midi floor board in another bank, If you use midi compatible fx you can assign them to change with the Triaxis presets. The use of midi offers a great advantage in versatility. Also Pair a Triaxis with a Mesa 2:90 and you can trigger the deep/ half drive/ modern voicing of the 2:90 on a per preset basis via the Triaxis as well.
Mesa Boogie Triaxis modes
Rhythm 1 & 2: Cleans to borderline break up tone
Green: Vintage Fat Rhythm, is the more vintage sounding “old Black Face Fender roots” Style circuit.
Yellow: Modern Bright Rhythm, roots from Mark IV,III, IIC+, tighter more urgent clean
Lead 1:
Green: Vintage Mark I lead
Yellow: High gain /Fat Mark I Lead
Red: Recto Vintage lead / depends on serial number different versions available
Lead 2:
Green: Midgain / Mark IV Lead
Yellow: Classic Mark II Lead
Red: Searing Mark III Lead
In the end this design is over twenty years old, it won't cover every base (nothing I've heard to date will at this point) but it will cover allot of ground if you are a Mark tone fan. I recently played with a Mark V for an hour or so and was very impressed with that amp however the Triaxis has some levels of flexibility that the Mark V can't touch like saving presets and midi, you find it, like it, save it and recall it anytime. The Mark V also has some levels of flex that the Tri can't do either like the push pull options, power settings more modes and twenty years to tweak it, still three sounds on tap, but very nice options for picking those within it's own limitations so really depends on your needs. The Triaxis still holds it's own after all this time, it's a quality instrument that was way ahead of it's time.
For me on the Tri I really enjoy both the clean modes and do my most my metal/rock high gain on lead 2 yellow and lead 2 Red basically Mark IIC and Mark III, the Mark tone also has great singing leads.
Everything else falls between those two extremes and it sometimes can be easy to fall into a rut when making your settings. I recommend reading the manual to help in dialing up the subtleties for the in-between gain tones, there is some real good tones in there.
You'll really need to try it out to know if it's for you.
I did finally after twelve years with the Triaxis decide to change things up a bit and build a Quad preamp 2:90/ Recto Racktifier rig with a voodoo lab gcx switchers and ground control and that rig offers yet again a different set of tone vs flexibility options.
However I likely would not enjoy hauling the quad/recto setup around do to it's weight. But that all depends on the situation.
A Mesa 2:90/ Triaxis/ fx processor/ midi floor board and a 2x12 cab is still relatively easy enough to haul around and is a good balance of flexibility, tone and size.
Personally I haven't played the Electradyne yet but have read great things about it.
If you want to run two amps like a Ed and a Recto that's all good as well.
I think it's really important to conceptualize what you really want in your rig. Draw it out on paper and think it through. Not just the amps themselves but everything you will need to make it work together, all of it.
Sometimes simpler is better.