The mod Naruto is using is completely different from what Bee is using. Kishi does not say everything in the manga, and the fandom does not accept fact from the anime. Otherwise, I recall in the anime, they made Bee say that the chakra mode would cost him his life. Why this was not stated in the manga, I think it make sense if the fandom learn to accept the facts.
In normal Jin-beast relationship, when the Jin take the biju's chakra, the Biju also take the Jin's chakra. the reason is that if the Biju does not replace the chakra, he will run out of ready to use stock, and they will end up in a pinch as we saw with Kyuubi and achibi. Naruto using his Uzumaki chakra can do the exchange with Kyuubi for some time, but its limited as we saw when Madara appeared. Then Kyuubi has to stop taking Naruto's chakra and give him free load. While Naruto can use the chakra mode with exchange for some time, Bee cannot do that because he does not have a lot of it. Another fact is that Kyuubi's chakra mode might also last longer than Achibi's chakra mode. Thus, to sum up, Naruto+Kyuubi's chakra mode last longer than Bee+Achibi's chakra mode whether with exchange between Jin and beast or not. The reason is that the first pair has a heavy load of chakra. However, the main reason is that Naruto's chakra is way larger than Bee's.
Concernin the marking on Naruto, the origin is unclear. The primary guess would be that it is due to the sealing technique used on Naruto. However, why the sealing will be transformed into a marking? This is really the unknown in the manga. My best guess is that Naruto underwent a transformation when he took Kyuubi's chakra. In fact, I argued that Naruto activated a new Jutsu when he took Kyuubi's chkara. This Jutsu is kind of KKG, and it is related to sealing. My first evidence is that the Rikudo seal is different from the initial Hakke Fujin, and better Naruto did it in a way that looked like he knew it before. This worked just like someone who unlock a certain level of knowledge just similar to Sharingan stages. Without going too deep in to speculation, I would say that Naruto is unlocking the same power that Rikudo had. We know that Rikudo could do sealing, but we don't know how he got it. Note also that since then, Naruto has been performing Justu easily, and even surpassing Minato lately in chakra control. It appears that Naruto's problem was the Kyuubi's will that was interfering with his mind before.
Let wait.