The advantage is that the road bike has more varied hand positions, so may be more comfortable on the trainer, and the tri bike lets you train in aero.

The downside is convenience. Swapping bikes on the trainer and dealing with chain grease is a pain.

Personally, I have my old road bike dedicated to the trainer....and put some clipon bars on it.

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I switch to the tri bike as tri season nears so I can do some training in aero and get used to the position. I have a noseless saddle on the tri bike so having it on the trainer gives me time to get used to that as well. After tri season ends I have a road bike on the trainer when I am training for gravel, fondos, and cyclocross.

I do most of my training indoors and have multiple bikes so I don't have to take bikes off the trainer very often.

You will be fastest on the bike that you train on, in the position that you train in most.

absolute fact - and the saddle you spend the most time on also becomes the most comfortable

Welllllll, I think you will be faster in the Tri bike than the road bike even if you train more often in a road bike but.......you will be faster on the Tri bike if you train more often on the Tri bike than you would be on the Tri bike if don’t train on the Tri bike.