Why would some people say that Connemara Irish is more innovative (and less conservative) than Donegal Irish? In what way would this be true, if at all?

Good question. At the dire risk of overgeneralizing, I've always had the impression that people of Connemara tended to shortcut a lot of the more stricter rules of pronunciation and incorporation of English (and other) words into the language than other dialect areas. I don't know if you could call it "innovative" as much as the natural course of language use for a certain population. I don't know so much about Donegal but what I hear I like, not so much different but as they have a great musical tradition up there, the language may reflect their desire to keep certain standards. I'm curious to see what others have to say, especially Bríd. I'd like to know more about it, too.

The verbs are more archaic in Donegal (especially the irregular ones).
The pronunciation as well (pronunciation of ll, nn and vowels before them and before m, rr... ; pronunciation of the endings too: -aigh is [ə] in Connemara most of the time).
Certain syntax features, eg. in Connemara they say "tá mé ag goil ag déanamh" vs. Donegal "tá mé ag gabháil a dhéanamh"...

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Yes I have noticed in my short time studying that in Connaught some words get contracted forms, like cad chuige to tuige, goil similarly. In Munster goil means weeping/crying I believe but I'm assuming it's used that way in Connemara also (only eight chaps into LI so far).

I too would love to hear from more people. Would anybody argue that Connemara is conservative in some ways compared to other dialects? It's not something I've seen said before.

So far we have Connemara: 'shortcuts'
Donegal: 'Certain verbs more archaic'

"Tuighe" is also used in Donegal.
I write "gabháil" in Donegal Irish because it's the etymological form but it's pronounced [gɔlʲ] just as in Connemara, we could spell it "goil".
Also the verbal noun of "goil" meaning to cry, is "gol" (goilim vs tá mé ag gol).

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne