Larry - your profile says you're close to Atlanta...I suggest a road trip to visit a couple of the maker spaces in Atlanta to see which of them can provide you with access to both a laser engraver and a CNC router.
Both machines have their strengths and weaknesses...it really depends on the results you're after. Earlier this week, I used a CNC Router to create custom pen boxes then laser engraved the name of each person that will receive one. I could have engraved them with the CNC Router (and have done that for other projects) but wanted the look/feel/speed of the laser this time.
I looked at the exact same text, same font, same computer driving all the work and noticed that the results would be better, and easier to accomplish, on the laser. The way the letters flow together in the font was handled better in CorelDraw (for the laser) than they were handled by VCarve/Aspire for the CNC Router. I could spend time forcing the CNC Router to do what I wanted, but went with the laser instead.
The cool thing with maker spaces is you can get access to expensive machines for a fraction of the cost....like using high end fitness equipment at a health club. You share access which helps keep the cost reasonable especially if you only need occasional access.
There are trade offs and downsides, but it's a great place to try both with training/support generally available...