I need some time to digest this, too. But I agree that a slogan like “Building a better Bitcoin” has advantages and disadvantages.
It is for sure bold enough to make people pause and maybe think about it (plus I like the alliteration
). If we can explain why Peercoin might be a better Bitcoin (and the environmental friendliness is for sure a good aspect!) then it might attract people rather than to affront them. Some will of course fight against that slogan and there are lots of arguments that can be brought forward against Peercoin.
One simple argument that will be used is the market capitalization. Peercoin (at the moment!) simply is not commercially important compared to Bitcoin. But this once more offers a lever to make Peercoin interesting. Because of the commercial success of Bitcoin there is a lot of money being invested in Bitcoin mining. Once miners realize that they can not mine Bitcoin profitably they might consider pointing their miners to a Peercoin mining pool. That is in fact one of the good reasons to directly compare Peercoin with Bitcoin: the PoW mechanism is the same!
…and they might think back to Bitcoins past when a Bitcoin was worth only a few bucks (in early 2011) and the might think about what could happen to Peercoin… Oh, you don’t want to make the same mistakes again, so maybe you don’t want to underestimate Peercoin! 
Another argument might be that Bitcoin can be used for paying goods and services whereas Peercoin is not that widely used. This is hard to counter, because Peercoin is in a too early stage to have such a reputation. It will for sure take some time until Peercoin is accepted by the same amount of places.
But even though Bitcoin is quite widely available (in comparison to Peercoin) it is not very common to pay with Bitcoin. Bitcoin is far from being a replacement of fiat money for daily use. So this is no big disadvantage of Peercoin.
I don’t want to go any deeper in a theoretical debate between Bitcoin and Peercoin because one other thought I share with MeBeingAwesome is the timeless beauty of slogans like “Just do it”. Once there is a well-known and accepted slogan like “Building a better Bitcoin” it will be hard to replace this with a timeless one. In the future it might be a mistake to compare Peercoin with anything else that might become less important than it is now. But to face the truth: Peercoin hasn’t really had a start yet. Don’t take me wrong; I don’t second the idea of Peercoin just because of a lame fanboyism. I really am convinced by the technical superiourity of Peercoin over Bitcoin (and I don’t only like Peercoin, but Primecoin, Litecoin and Novacoin as well; that’s a different story…). I’d like to see Peercoin be successful. Considering the power comsumption of Bitcoin mining hurts.
Those who already know in detail about Peercoin and still stick to Bitcoin can hardly be convinced of Peercoin. And that’s ok. They are free to come to their own conclusions. But those who stick to Bitcoin because they don’t know about other crypto coins might be convinced of Peercoin.
And before you can convince them, you need to direct their attention to Peercoin!
So for the current stage it might be no bad idea to jolt someone from Bitcoinism by claiming that Peercoin is a better Bitcoin.
…this post might be edited later once I had time to think about this. Consider this my first, barely structured impression about the slogan 
[edit]
Rereading the post revealed some typos and one semantic error; corrected. I still think that “Building a better Bitcoin” has some flaws, although I don’t know a better slogan yet. For the time being I think “Building a better Bitcoin” bites more off Bitcoin than Peercoin can chew…
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