Pro's and Con's to each one.
Aspen Grove:
Steeper but shorter.
Passes by Emerald Lake.
Trail crosses more waterfalls.
Amazing views the entire way as you hike up.
Timpooneke:
Trail is more gradual but longer.
Emerald Lake must be done as a side trip.
Best views are really once you make it into the upper basin 75% of the way to the summit.
KILLER wild flowers when in bloom.
I prefer to backpack Timp. Last time I did it we went up Timpooneke, dropped our packs at the saddle, hit the summit, grabbed our packs, and traversed to Emerald Lake where we camped before heading down in the morning.
DONT HIKE IT ON A FRIDAY/SATURDAY! The traffic is literally insane especially considering how long it is. I have hiked up on a few Saturday afternoons and camped into Sunday and only seen 1 or 4 other tents. That leaves plenty of space for privacy. Friday nights can have 10-30 tents but they all have to make it back to church on Sunday

Also, never NEVER camp by the rock shelter near Emerald Lake. Its big thing for people to start the hike and midnight and summit by sunrise. These people tend to make long pit stops at 3-4 am on the way up in the hut and they are always really loud.