The ingredients differ slightly (taken from Burtsbees.com). As far as I can see, the tube contains sunflower seed oil while the tin contains sweet almond oil, and that's the only difference.
Tube: cera alba (beeswax, cire d'abeille), cocos nucifera (coconut) oil, helianthus annuus (sunflower) seed oil, mentha piperita (peppermint) oil, lanolin, tocopherol, rosmarinus officinalis (rosemary) leaf extract, glycine soja (soybean) oil, canola oil (huile de colza), limonene
Tin: cera alba (beeswax, cire d'abeille), cocos nucifera (coconut) oil, prunus amygdalus dulcis (sweet almond) oil, mentha piperita (peppermint) oil, lanolin, tocopherol, rosmarinus officinalis (rosemary) leaf extract, glycine soja (soybean) oil, canola oil (huile de colza), limonene
If you're deciding between tin or tube, well, the tin looks prettier and contains more product for the price, but it's kind of unhygienic to use your fingers and application is time-consuming. Plus if you bring it around, the tin will get banged up. For me, I'd prefer the tube for the ease of application even though it contains only half the amount of product for the price, also because I'm a hygiene freak and it's troublesome ensuring my fingers are clean before using the tin version. What I do right now is that I carry the tube with me all the time, while I keep the tin at home to use before bedtime, so the tin remains quite pristine.
You know, lipbalms are the kind of cheap thing that you'll keep buying a lot of, from different brands, just because they're cheap and there's so much variety! But I can see that Burt's Bees will be something I'll go back to over and over again, and always keep a back-up tube of. Sometimes I find it annoying when I find a HG (holy grail) item like that though, because I feel like I won't be able to try other products. Is that weird? :P