Zion and Bryce... which to do first
 

Planning a trip starting in Las Vegas and ending up in Sedona. My plan so far is:
Las Vegas-2 nts
Zion-2 nts
Bryce-2 nts
Page/ Lake Powell - 1 nt
Sedona-2 nts
Someone suggested it might be better to do Bryce first and then backtrack to Zion because it would take me through the eastern entrance to Zion which is apparently not to be missed. Does this make sense? Is it worth the extra driving time?
Also should I take a day from Bryce and add that extra day into Zion or Lake Powell?
Thanks in advance for any suggestions.

No, it does not make a difference.

You can easily see the iconic views regardless of which you visit first.

You'll drive through Zion and see the eastern entrance on the way to Bryce. It's more the drive than the entrance itself, and as @J62 says, you can stop to see the view. It also doesn't make any sense to do Bryce first if you are moving on to Page, and it will add additional driving time. You had the itinerary right from the beginning; keep it that way.

Ok great. I will. Thanks so much!

These are the main sights of interest along the road towards the east entrance, in order of priority.

#1. Canyon overlook trail - parking just east of the tunnel

#2. Tunnel. you can't avoid it. But you may need to wait as large vehicles (RVs) need to drive down the center line so they limit traffic to one-way only when there's an oversized vehicle.

#3. Switchbacks west of the tunnel. Again, you can't avoid them. Worth stopping at one or two to enjoy the view. Better yet, ride down that section on a bicycle in the early morning hours when there are no vehicles. Just be sure your brakes work. Fun!

#4. The landscape between the tunnel and the east entrance. Very different from Zion canyon. Worth a short stop just to check out the remarkably different terrain.

I would vote for an extra day at Zion. Bryce is nice but can be seen in less time.