It's good for both of them because they can fuse their feats and accolades for use on one another; Plagueis has his feats and the most powerful ever quote, Sidious has backwards scaling from RotS.
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The only concrete evidence we have, to my knowledge, that Sidious is more powerful in RotS than TPM is "the greatest master of evil ever to use sith power" quote, which then states that "his power grows". But I think it would be rare for a Force user to grow substantially more powerful from their fifties to sixties, especially since Palpatine doesn't seem to have much time for training; there's not much precedence for it except for Dooku, who was learning the dark side largely from scratch and so would have lots of room. Sidious's boost would come from Plagueis's death; then he probably made marginal gains through RotJ, and a noticeable leap to DE.
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We know Sidious continues to perform rituals between TPM and RotS. And whilst he's in his fifties, we're forgetting that his potential is basically second to to nobody except the Skywalkers.
But indeed, he should be very close to RotS Sidious by this point. I'd imagine that there's more of a gap between RotS-RotJ or RotJ-DE Sidious than TPM-RotS.
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There's also this: For a decade, there was no physical signs of the remaining Dark Lord, but evidence of his power began to appear.
The Jedi ability to use the Force inexplicably began to diminish.
–Databank (old): The Jedi Order
Even though TPM Sidious was already a galaxy-wide nexus at the end of TPM, the Jedi's ability to draw on the Force only started being hindered around AotC. That'a a clear sign of a power-growth in Sidious.
There's no explicit proof that any of the rituals increased his power, but we've seen him perform a variety of rituals (Sithisis and TCW are worth mentioning), so I'd imagine that he does get stronger in some cases. And a ritual like the one in Sithisis could well make him more powerful. So it is plausible, though not proven, that he increased his power through such rituals. I mean, we know, Vitiate grew stronger through "exploring the uncharted and most sinister depths of the dark side" and his age would suggest that he had achieved more of his potential than Palpatine as of TPM had. So it makes sense that Palpatine would grow stronger in the same way.
My intepretation of the Sithsis ritual was that he was channelling the negative emotions of the Jedi into that crystal, which then produces a Sithspawn that devours him, and triggers some kind of rebirth. Would make sense that he was absorbing that energy into himself.
It seems like rituals such as that one were necessary for him to keep up his appearance as Chancellor Palpatine. He presumably stopped that after RotS and kept his true appearance.
Which is why he abandoned such practices after RotS, when he no longer needed the persona of Palpatine.
Beforehand, I'm sure he'd have gone to any lengths to maintain his appearance. And as Azronger said, his power was likely so great that the corruption transcended typical concealment methods. Remember that Palpatine also had to mask his immense power entirely, and make himself appear non-Force sensitive.