Not really ... increased power consumption if you leave both screens on?
When I used my laptop, I always had it hooked to a screen at home, as do a lot of people I know. In fact there are a lot of advantages to hooking your laptop up to a monitor (and possibly keyboard/mouse too). Increased viewing space, less wear on laptop screen. Plus the keyboard/mouse gives you greater control and more ergonomic typing. Frankly the only time I wouldn't have mine set up that way would be if I were on the couch or out of the house/office.
You're talking about the differences between two screens. There will be differences in color, resolution, response time, power consumption, clarity, etc. It all depends on what laptop screen you have and what monitor you're planning on using.