Looking at your existing applescript code this should sort any files you've selected by last modified date and return the latest result into a dialog box for you:
set dateList to {}
tell application "Finder"
set inputList to get selection
repeat with i from 1 to count (inputList)
set end of dateList to get modification date of item i of inputList
end repeat
end tell
--Compare section...
set modDate to item 1 of dateList
repeat with i from 1 to count (inputList)
if dateList's item i > modDate then
set modDate to dateList's item i
set theResult to displayed name of item i of inputList
set theResultDate to item i of dateList
end if
end repeat
--Display Result…
display alert "Most recently modified file in selection:" message "" & theResult & "
" & theResultDate