Courtesy:Sri.Dhananjay Vaidya & HN.Bhat

यमुनातीरविहारी is a tatpuruSha compound
यमुनातीरविहारः is a bahuvrIhi compound. (The problem is because we do not currently read saMskRta with svara accents. Without svara accents, this word could also be a tatpuruSha meaning "picnic on the bank of the Yamuna", rather than the bahuvrIhi "one who picnics on the bank of the Yamuna".)

Both are used in respect of Krishna, and it depends on the need of the lyrics:

Here it is यमुनातीरविहार, नवनीतदधिचोर,

makes the alliteration melodious which is a music composition, by Bhadracala Ramadas.

while the other link I had already posted,

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यमुनातीरविहारी बृन्दावनसञ्चारी
गोवर्द्धनोद्धारी गोपालकृष्ण मुरारी (यमुना…..)

makes it melodious with alliteration, than any Grammatical consideration as in the last word , मुरारी which is not strictly Sanskrit grammar binding.

In a stotra, as Sahasranama, both will make equal in meaning, but the difference will be in the नामावलिः - which is variably put into चतुर्थी with नमः, as @विहारिणे नमः or @विहाराय नमः।
as both are acceptable forms in the stotra. But preference will be ॒विहारी so that there is no room for any doubt whether it is bahuvrihi, or karmadharaya. And it is advisable to avoid such doubtful compounds except needed for श्लेष or यमक, by poetical consideration of the classical Sanskrit literature.

न कर्मधारयो बहुव्रीहिप्रतिपत्तिकरः । ।काव्यालंकारसूत्र ५,१.७ ।
तेन विपर्ययो व्याख्यातः । । सूत्र ५,१.८ । ।
according to Vamana.