Hi ... for me, it depends on the song. For most songs, I "do my own thing" although I like to have it sound "reminiscent" of the original, but not identical. If a song has a 'signature' lick, I try to include that or something close to it. I do tend to try to select styles and sounds that are similar to the original, esp. for 'key' or 'signature' parts. For solos (say, guitar or sax or trumpet), for some songs I'll play something pretty close to the original, for others it's totally "my own". Just depends on the song and my feeling at the moment etc.

Examples (random thoughts that occur to me at the moment) ... when I play "Just The Way You Are", I tend to play the sax solo very close to the original. When I play "All Of Me" and I play a sax or trumpet solo, it's completely improvised. When I play the guitar solo [on Tyros5] to "Stairway to Heaven" (yes, I do play that occasionally if requested!), I play it nearly identical to the original. When I play a guitar solo in something like "Kansas City" or "Sweet Home Alabama", it's improvised.

For classical pieces or anything older than 1900 (20th century), I try to have the melody be "very close to as-written", and the chordal part of it "about right" (close to as-written or as-heard-played-by-orchestras) with less improvisation than when I play popular music from 20th century.

-Jim