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##Seriously, 10 bytes

,û,Z`M`MΣù

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Uses the same strategy as Martin's CJam answer

Explanation:

,û,Z`M`MΣù
,û          get first string, uppercase
  ,Z        get second string, zip with first string
    `M`M    map maximum
        Σù  join and uppercase

Seriously, 10 bytes

,û,Z`M`MΣù

Try it online!

Uses the same strategy as Martin's CJam answer

Explanation:

,û,Z`M`MΣù
,û          get first string, uppercase
  ,Z        get second string, zip with first string
    `M`M    map maximum
        Σù  join and uppercase

##Seriously, 10 bytes

,û,Z`M`MΣù

Try it online!

Uses the same strategy as Martin's CJam answer

Explanation:

,û,Z`M`MΣù
,û          get first string, uppercase
  ,Z        get second string, zip with first string
    `M`M    map maximum
        Σù  join and uppercase

##Seriously, 10 bytes

,û,Z`M`MΣù

Try it online!

Uses the same strategy as Martin's CJam answer

Explanation:

,û,Z`M`MΣù
,û          get first string, uppercase
  ,Z        get second string, zip with first string
    `M`M    map maximum
        Σù  join and uppercase

##Seriously, 32 bytes

,;`l`MM╗`;l╜-'.*@+`MiZ`i@'.@Æ`MΣ

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Explanation will be added after more golfing

##Seriously, 10 bytes

,û,Z`M`MΣù

Try it online!

Uses the same strategy as Martin's CJam answer

Explanation:

,û,Z`M`MΣù
,û          get first string, uppercase
  ,Z        get second string, zip with first string
    `M`M    map maximum
        Σù  join and uppercase