I'd split between the 2; they're very different and complement each other well. Fly in to Guatemala City, spend a week or so in the highlands - few nights in/around Antigua and the rest on Lake Atitlán. Then head to Tikal via either Rio Dulce/Livingston or Lanquin/Semuc Champey and cross into Belize. Depending on your interests you could spend most of your time in either country. Highlights for me in Belize are the caves and hiking and ruins in western Belize and blue water time. Caye Caulker is a cool place to end a trip; if you want more time on the water and don't mind roughing it, consider Glover's Atoll for a week. You can read the blogs and travelogues linked on the main pages of my photo collections below.

You need guidebooks - Moon is good for both countries plus Rough Guide for Guatemala and Fodor's for Belize.
Happy planning!
http://www.flickr.com/photos/staceyholeman/collections/

Oh - the weather: it's the rainy or 'green' season in July. Expect beautiful mornings with rains some afternoons (highland areas) or typically evenings/overnight (low lying areas). Technically it's hurricane season but big impact storms are rare that time of year. I travel in the region every summer and find it to be a great time to visit - last year I split between Guatemala and Honduras, this summer 6 weeks split between Guatemala and Belize.

We've been to Belize in July, and we got rain every day but not an all day rain. I'd go back during that time frame.

Thanks very much, Hopefulist and Volcanogirl! To travel between Guatemala and Belize, do you fly or is there a cheap bus?

Either - depends on which you have more of, time or $. The night buses between Guatemala City and Flores (near Tikal) are popular and there are both local and express buses heading west from there into Belize.

Weather in Belize
In July, the southern region (Placencia, Punta Gorda) can be VERY wet -- it's the wettest time of the year. It's not as bad further north, but I've never experienced rain EVERY day (I live here). Rain tends to be brief showers and usually falls in the early morning or overnight, and the days are fine.

Transportation
I hope it's OK to add this link to the Belize Bus & Travel Guide (free & no advertising):
https://belizebus.wordpress.com/
It has schedules for the express buses between Flores & Belize City, water taxi information, and links to the regional airlines.

Hi Hopefulist,
You mentioned in another post your favorite hotels in Guatemala are $20-30/double - could you list what they are and if you have other affordable recommendations for Belize? Thanks!

:: In Antigua: www.casa-cristina.com

:: In Panajachel: Mario's Rooms (No website, the phone number is 7762 2370 (dial 011 502 first if calling from the US, don't expect English)

:: In San Pedro La Laguna: http://hotel-sakcari.com/ and www.mikasohotel.com

:: In Flores: La Mesa de Los Mayas (No website, but here's the email address I used: mesamayas@hotmail.com )

:: In San José Succotz, Belize (west of San Ignacio): www.thetrekstop.com

The rest of the places we've stayed in Belize have been more expensive, partly because it's really hot there and sometimes we've chosen to stay in more upscale places. Also, a few favorites aren't there anymore. Here's a list of my favorite Belize sites (not just lodgings). Happy trails!
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My photo collections with blog, travelogue, and review links: http://www.flickr.com/photos/staceyholeman/collections/

My descriptions and reviews on Trip Advisor:
http://www.tripadvisor.com/members-reviews/hopefulist

Guidebooks I like: Moon Handbook, Fodor’s Guide, and Explorer’s Guide.

Laminated identification cards: http://rainforestpublications.com/belizeFieldGuides/index.html

A very cool checklist book for Belize for the young or young-at-heart: http://www.amazon.com/Play-Belize-Mesa-Somer/dp/0615198546/ref=sr_1_2?ie=UTF8&qid=1330549187&sr=8-2
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Budget to midrange lodging site: http://www.belizeexplorer.com
Great island and lodging downloads: http://www.belizefirst.com
Informative transportation blog: http://www.belizebus.wordpress.com
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Shuttle recommendation: http://www.parrot-nest.com/belize-shuttle.html
Zoo: http://www.belizezoo.org
Great jungle camp in Cayo: http://www.belizecamp.com
Great budget lodging in Cayo: http://www.thetrekstop.com
Great value hotel with pool in Cayo: http://www.aguadahotel.com
Don't miss cave trip: http://pacztours.net/actun-tunichil-muknal/
Lodge with lots of adventures: http://www.cavesbranch.com
Great inn in coastal Garifuna town: http://www.hopkinsinn.com
Garifuna drumming center: http://www.lebeha.com
Apartment on the beach on Caye Caulker: http://www.staycayecaulker.com/sailwinds.html
Great day snorkeling trip: http://raggamuffintours.com/hol-chan-snorkel/
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Very rustic atoll experience, cheap if you have a week: http://www.glovers.com.bz/
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My favorite hotel at Tikal: http://www.tikalinnsunrise.com
Fabulous, fun tour guide: http://www.tikalroxy.blogspot.com
Favorite midrange places in Flores: http://www.corpetur.com
Good value budget option in Flores: La Mesa de los Mayas
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Here are the places we’ve decided to stay this summer, all new to us but carefully researched:
Another Caye Caulker option: http://www.gocayecaulker.com/accommodations/maxhapan-cabanas
Another, less-visited cave option: http://www.actunchapatadventure.blogspot.com/
Highly reviewed jungly place near Punta Gorda: http://www.hickatee.com
Rural Toledo village visit and guesthouse organization: http://www.teabelize.org/index.php?id=32
Off the beaten track diving and snorkeling, Sapodilla Cayes: http://www.reefci.com
Rental apartments in the heart of Placencia: http://www.oneworldplacencia.com
Secluded resort on N. Ambergris Caye with snorkeling from shore: http://www.tranquilitybayresort.com