Both of these trees have transformed significantly since WoW Classic, and Shamans are currently in the fortunate position of having three raid-viable trees all capable of contributing differently. The incoming WF nerf will decrease enhancement DPS by approximately 15% (discussed @ The Change to Windfury and You! (does not apply to warriors)), significantly altering the relative positions of the two dps trees shamans have. Let's compare the two trees.


Elemental

Viable in PvP and PvE
Excellent single-target and above-average AoE dps
Controllable burst
Sustainability increases with gear quality (spellcrit = free spell)
Decent spot healing potential (dmg/healing and spellcrit add to heals)
3% spellhit and 3% spellcrit for your group
100% of damage scales with gear
-10% threat, 130% threat required to pull

Enhancement

Viable in PvE, weak in PvP
Excellent single-target, below-average AoE dps
Uncontrollable burst
Sustainability increases with gear quality (int and mana/5)
Poor spot healing potential (virtually zero +dmg/healing)
10% AP for your group
~80% of damage scales with gear (WF and white hits)
-15% threat, 110% threat required to pull


Given that Enhancement is generally a more restricted, less flexible talent spec, which DPSes from melee range and has a lower threat cap, it's expected that it will have a higher raw DPS than Elemental. Previously this was not necessarily the case as Elemental's DPS was coupled with extremely poor sustainability, but recent changes have made both playstyles functional in even the longest boss battles.

A few months ago things were very different. As it stands now, I'm afraid that a significant nerf to Enhancement dps on top of the recent Elemental buff will kill the spec in endgame PvE; maybe not at blue gear levels, but scaling may cause Elemental to pull way ahead of Enhancement when players are in Tier 6.