I was in Guatemala and Honduras last summer. The answer, in short, is 'it depends'. The main tourist areas of Guatemala should be safe enough (i.e. Antigua, Tikal, Lake Atitlan etc). Especially Antigua seems very safe, and I wouldn't worry about any violent crime (there are always exceptions of course). As you may know, Guatemala City has its security issues, but it depends on where in the city you want to go. Most travellers seem to stay away from the capital, and a friend I have from the city would never take either local buses or taxis there. She belongs to the local elite though, and they tend to exaggerate security issues. I did notice a heavy police presence as I travelled through the city in a bus, that is not really a good sign.
As for Honduras, i mainly visited Utila, which is very safe and westernized (dive location). I've heard bad things about some places in Honduras (San Pedro Sula springs to mind), but I didn't have any troubles travelling through the mainland. Seek other sources for more information on mainland Honduras. over 8 years ago
Recently there have been a lot of controversies within Belize and Honduras. I have spoken to people from Honduras and they said with the government, they wouldn't travel right now. Belize is find in the tourist areas, but you don't want to travel to far away. If your Spanish is good, then you are a bit better off. I wouldn't travel between the countries, except by plane, which is pricier. over 8 years ago