The only feature the layout module supports is drawing free-angle lines from one point to another. It's a lot easier to say that than to list the hundreds of absent features considered standard in any PCB CAD program.
If your experience with electronics progresses at a normal rate, there's a very limited amount of time you'll even care about a breadboard design tool. Breadboards (physically) are design tools already, no one spends any time doing CAD to figure out how they are going to wire up a breadboard. Most of my designs go straight from a schematic to a PCB. If I use a breadboard it's typically very temporary, to test a few concepts that I want to verify while designing a schematic, usually in the analog domain.
I've only been designing PCBs for 7 or 8 years, non-career, so I'm probably in the bottom 10% of PCB designers experience wise. However I've used quite a few different tools and eventually settled on Eagle having the mix of features and price I found acceptable. Started with freeware and eventually bought the pro version.
Doesn't really matter which one you choose, though, as long as it has the basic set of features and you spend time getting used to it. Some people do very well with gEDA. Other swear by Kicad. Some (shudder) like ExpressPCB or PCBArtist and lock into a single proto supplier.
I would say that if you spend a lot of time in Fritzing you will eventually realize, if you plan to design real PCBs in the future, your time would be better spent learning some other tool.