Constructing expressions using Sum vs Array[... Plus] vs Plus@@Table[...]

This is something that you could have tested yourself, quite easily. I sugest the use of RepeatedTiming for more reliable measurements.

BarChart[
 {
   First@RepeatedTiming[
     Sum[f[i], {i, 1, 100}]
     ],
   First@RepeatedTiming[
     Array[f, 100, 1, Plus]
     ],
   First@RepeatedTiming[
     Total@Table[f[i], {i, 1, 100}]
     ],
   First@RepeatedTiming[
     Plus @@ Table[f[i], {i, 1, 100}]
     ],
   First@RepeatedTiming[
     Plus @@ (f /@ Range[100])
     ],
   First@RepeatedTiming[
     Total[f /@ Range[100]]
     ]
   } 10^6
 , ChartLabels -> {
   "Sum",
   "Array[_,Plus]",
   "Total@Table",
   "Plus@@Table",
   "Plus@@Range",
   "Total-Range"
   }
 , PlotTheme -> "Scientific"
 , AspectRatio -> 1/2
 , FrameLabel -> {"Method", "Time \[Mu]s"}
 , ImageSize -> 600
 ]

Sum isn't really for constructing expressions: it's primarily for finding an analytic formula that represents a sum. It's mostly useful when bounds are unknown or infinite:

Sum[1/2^i, {i, 1, n}]
(* 2^-n (-1 + 2^n) *)

Mere expression construction can't do this.