Nikon 3100 is essentially the same as my D3200, and is pretty much all you would expect or hope of a proper DSLR. The Panasonic Bridge is almosty identical to my other half's Nikon DC3100 bridge, except the Panasonic has some manual control modes.
Either work pretty much as a "point and press", and for an awful lot of the time, the camera will get things more right more often than you will going to manual modes, and likely to get them wrong.
The bridge has a few very useful things going for it. First is its cheap. depending on deal you get 1/3 to 1/2 the cost of the SLR, and you get a heck of a lot of zoom with it. Covers the range of a pair of kit lenses. But its not interchangeable. I cant find details in the spec to suggest it has a filter thread on the lens, so I would presume not (O/H's Nikon doesn't either) This means you cant use accessory filters, if you have the inclination... well, not easily. Nor can you manually focus.
But, its fairly small, fairly light and quick and easy to use. Pixel count, ISO range and lens appature are pretty good, and not much different to that of the SLR, though the shutter speed range is a little limiting, goes down to 15seconds for long exposures, but no 'bulb' setting for timed exposures for longer.
Either, I'm sure would do an awful lot of what you want, for an awful long time. And if I am honest, I could hapily live with the bridge... I have lived with a much lesser compact for an awful long time.
The SLR, will come into its own, though if/when you want to do more 'specialist' stuff, where you need the extra versatility and control it offers; say really close up macro photo's, long exposure stuff, or push into places where you want faster or longer lenses for capturing far off subjects, fast moving subjects, and or in lower light situations.
Bigger, bulkier, more unwieldy and less likely to be so 'handy' when a photo oportunity arises, its a lot of extra expense, for a small amount of extra potential you possibly wont be able to readily benefit from very often, and a little bit better 'clarity' in the image quality that comes out of it.
I really cant say which would be the better bet... I really dont know what you hope to do with it, or what your level is, or where you want to go, or how fast.
I bought the D3200, becouse I'm no novice, and know what I might do with an SLR, and could utilise a lot of it very quickly. But, being honest, I know that the bridge would take probably 3/4 of the pictures I would ever want to look at, without even switching it off 'smart' setting. Incredibly tight fisted, only thing that stopped me buying one and saving probably £250... was a perversion of outlook, where rather than being gleeful at having saved £250, I'd be ruing 'wasting' £120 on a camera that ISN'T an SLR.... ie did nie on everything but bolster my ego!
Sort of hints the Bridge is a good starting point.... BUT? If you are thinking of picking up fairly fast, and getting experimental, perhaps doing a course; then SLR may be the better bet, becouse as soon as you start trying to go 'manual' and doing the thinking instead of leaving it to the camera, the limited control and versatility of the bridge is likely to become a frustration. I know it is for my O/H wanting to do 'more'... but then I can hand her my SLR for the few instances she wants to try things... and I can grab her Bridge when the kids do something amusing! THAT is the sort of difference you're looking at.