Both the reconverting bank and the bank that presented the substitute check to your institution are liable to the drawee bank under the warranty and indemnification provisions. Assuming they are different institutions, you do have a choice as to which one you assert a claim against.
The reconverting bank would seem to be the most logical target, because they presumably have an agreement with the truncating bank and should be the quickest route to obtaining a better copy or even the original check. However, it has yet to be established what kind of treatment banks will afford one another on the claims process. You might choose to go back to the bank that presented you with the substitute check because you have an ongoing relationship with them and might expect better treatment.
(If a logical decision was made about how to present the item for payment, in forward presentment it is likely that the reconverting bank will also be the bank that presented the item to you.)
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.