This is a tough one!  We enjoyed both places immensely and keep going back and fourth on which one was better.  Here's a breakdown of each.  Pictures of Bagan are on the left and Angkor is on the right.  Our cover photo is from Bagan, so maybe we're a bit biased.  :) 

Entrance Fee

Bagan: $20 for 5 days

Angkor: 1 day pass = $20, 3 day pass = $40, 7 day pass = $60
**These prices are going up on February 1st, 2017.  The 1 day pass will be $37, the 3 day $62, and the 7 day $72.

Transportation

Tuk Tuk: This is the most popular way to get around in Angkor and a ton of fun!  A knowledgeable driver will take you around for a stress free day of navigating the sites.  It will cost you $15-$20 for the day, maybe a bit more for the further temples.  There are tuk tuk's in Bagan, as well, but they will stick to the main roads.  

Motorbike: If you have a motorbike license, you can rent one in both places fairly easily and it's enjoyable to get around on your own. 

E-Bike or Electric Bike: There are loads of e-bikes all over Bagan for as little as $4 a day.  They're easy to operate and can fit two people nicely.  You will see quite a few people (especially couples) with this mode of transportation.  You can go anywhere off the regular roads and find your own temples to explore.  Angkor only has a few e-bike rental shops but they charge $10 a day per bike and the bikes only hold 1 person.  We only saw a few people riding them around Angkor.  

Horse and Carriage: Fairly popular in Bagan but a slower way to get around the temples.  It might be a bit uncomfortable when not on the main roads.  We didn't see any horse and carriage rides in Angkor but I'm sure they have them. 

Bicycle: Very cheap and easy to rent in both places.  You will be riding much further distances in Angkor (especially to get to the main temple area) but the roads will be nice and paved.  In Bagan, only the main roads are paved at the most popular temples.  If you want to explore some of the more remote temples, you will be riding in dirt or sand.   

Taxi: Easy to find in both places but not the best way to get around.  You will pay more and won't experience the sites, sounds, and smells like you would if you were on a bike or in a tuk tuk. 

Proximity to town

Bagan has 3 main towns; Old Bagan, New Bagan, and Nyung- U.  They are part of Bagan's archaeological zone, making it easy to access many temples from the main road or just minutes from your hotel.   

The entrance to Angkor Archaeological Park is about 3km north of Siem Reap (the main town), or about a 20 minute tuk tuk ride.

Geography and Climate

Bagan: Vast plains, arid, smaller trees and shrubs, very chilly in the morning and evening and hot in the middle of the day.

Angkor: Jungle, very humid, massive trees and vines (many overtaking the temples themselves), a bit cooler in the morning and evening, but absolutely sweltering during the day.

Sunrise/Sunset

I have to say that Bagan wins ten fold on this one, especially for sunrise.  You can choose any temple you want and make the climb up to the top for an excellent view of the plains with dozens of temples below.  As the sun starts to rise, so do the hot air balloons.  It's absolutely magical.  There are a few good spots to congregate for sunrise/sunset in Angkor, but you won't get a view of all the temples and you will be fighting with the crowds. 

Accommodations

Cheaper and more to choose from in Siem Reap (Angkor) due to the hoards of tourists pouring in.  Our hotel was less than $20 a night.  You can still find cheap accommodations in Bagan for around $25 a night but the options are much fewer. 

Religion and Architecture

Bagan: Buddhist

Angkor: Hindu and Buddhist (some temples are one or the other and some are a mix of both). 

Number of Temples

We couldn't find exact numbers for either place but Bagan definitely has a lot more.  We read that there were over 3000 temples at one point and about 2200 remaining today.  Some say there are more temples in Bagan than tourists.  

The temples we saw in Angkor were mostly large, sprawling complexes.  We read there are over 1000 but many of them are reduced to rubble these days.   

Overall Feel and Cultural Experience

The temples of Angkor are grandiose and sprawling.  You can weave in and out of different rooms, not knowing what you'll find next.  Unfortunately, the swarms of tourists make it feel a bit like Disney World.  We were frequently stuck between tour groups and people frantically running around to take pictures. There is somewhat of a disregard for the dress-code and cultural respect in general.  The vendors selling souvenirs, food and drinks were much more aggressive in Angkor, as well.  

When visiting Bagan, it feels like a well kept secret.  The temples of Bagan are similar in shape and style but there are many more to explore.  There aren't a lot of tourists and you can find many temples off the beaten path where no one is around.  Sure, there are bigger crowds of people at some of the more popular temples, especially during sunrise and sunset, but it's nothing compared to the crowds at Angkor.  In Bagan, you are required to remove your shoes before entering any of the temples and you must have your shoulders and knees covered.  Every tourist we saw respected this to the utmost.  People were calm and collected and didn't make a scene with their cameras.  I'm sure this will change in the years to come, but for now it's a special experience.