I like to use rigid XPS foam on basement walls but usually only install 1" thick sheets. We often then frame on the interior side of the foam and install standard fiberglass batt insulation in the new bays. (Note no vapor barrier on the interior of the wall assembly.)
The price is right, if you use tongue and groove, it can be fitted quite tightly together and to the floor very quickly, is a good vapor barrier/retarder, and is extremely moisture resistant.
I don't think I have heard or read any arguments claiming batt insulation alone would be a better option. There are superior but more expensive ways to go such as spray foams or pre-built basement wall systems, but there is almost always a cost/benefit decision for every client, and you have to decide what is reasonable for you.
I see that you have been doing your homework, but have you read the Building Science articles on basements?
Follow up questions to you from a contractor would be: how wet/dry is your basement, are you insulating the floor or the basement ceiling, what are the foundations walls like, i.e. straight or smooth, will they hold fasteners, how much basement wall is below and above grade, and are your framing or planning on attaching wall board straight to the XPS?
Have fun with it.
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